Matrix Modern

October 23, 2009 12:18 pm | art deco sofa

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Matrix modern
Matrix modern
Modern Abstract Algebra Proof - any help would be greatly appreciated?


Let H be the subset of M2(R) consisting of all matrices of the form [ a-b]
[b a]
for a,b belong to R

a.) show that is isomorphic to
b.) show that is isomorphic to

For ease, I'm going to denote that matrix [a b] instead of it's normal 2x2 representation.

You want to use the isomorphism:

φ( [a b] ) = a + b i

This is clearly a bijection. All you have to do is show that it is a homeomorphism, and to do that you need to prove:

Part a: φ( [a b] + [c d] ) = φ( [a b] ) + φ( [c d] )

Part b: φ( [a b] * [c d] ) = φ( [a b] ) φ( [c d] )

PART A:

This will be pretty trivial. First find [a b] + [c d]

[a -b] + [c -d] = [a+c -b-d ]
[b  a]    [d  c]    [b+d  a+c ]

This means [a b] + [c d] = [a+c b+d].

And so φ( [a b] + [c d] ) = φ( [a+c b+d] ) = a+c+(b+d)i

Now look at φ( [a b] ) + φ( [c d])

= a + bi + c + di = a+c+(b+d)i

So we conclude φ( [a b] + [c d] ) = φ( [a b] ) + φ( [c d])

Thus this is a homeomorphism and since it's bijective, we know this is an isomorphism.

PART B:

First find [a b] * [c d]

[a -b] [c -d] = [ac-bd -bc-ad ]
[b  a] [d  c]    [bc+ad  ac-bd ]

Which means [a b] * [c d] = [ac-bd ad+bc]

Thus φ( [a b] * [c d] ) = ac-bd + (ad+bc) i

Now we look at φ( [a b] ) φ( [c d] )

= (a+bi)(c+di) = ac + bci + adi + bdi²

= ac + (bc+ad)i - bd = ac-bd + (ad+bc)i

Thus φ( [a b] * [c d] ) = φ( [a b] ) φ( [c d] )

And we know it's an isomorphism (bijective homeomorphism).

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Modern Jazz: Matrix (Suite)

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Comments

Action films have become post-modern parodies of themselves. I wish I'd burned my DVD player after seeing the Matrix for the 1st time.

/ ITtelligenceDir
August 24, 2010, 11:33 am

First day of sophomore year- physics 2, comfy chair, modern bio, matrix algebra. Welcome back!

/ LostSheepProd
August 27, 2010, 10:08 pm

The ultimate measure of a person is not where one stands in moments of comfort and convenience, but where one stands in times of challenge and controversy:
Dr. Martin Luther King Jr.

IT’S TIME TO WAKE UP

People who try to maintain and create empires do it by manipulating the people that they are trying to conquer. They go out of their way to make sure that the people that they’re attempting to conquer is perpetually misled and manipulated. Therefore the conquered group’s perception of reality is not their own. It is shrewdly imposed upon them without them even knowing it.

It is time that more African Americans wake up to these realities.

“The way in which you destroy a group is by getting them to destroy themselves by dividing their ranks against each another. And then you feed these divided ranks inflaming misinformation that leads them to kill each other off.”

Certainly you have asked yourself why is that African Americans are so is inundated with negative imagery's of themselves. It is so unrelenting that it leads many to embarrassingly ask themselves the questions of damn are we Blacks really that bad?

It is actually a mass media social manipulation program of where in which African Americans are being covertly psychologically conditioned-through a white controlled media that subjects them to seeing only the fraudulent worst in themselves. Its motto is Divide and conquer. It drills the message into the black psyche that we are powerless, of lesser moral, and intelligence and that we cannot govern ourselves –therefore needs whites to govern over our lives. It is designed to totally detached African Americans from their sense of power and reality. Furthermore, it is all a massive lie. We are a powerful beautiful and extraordinary people.

When people in power wants to suppress or to exploit a group they do so by portraying that group as a fearsome enemy or a major problem of the society through lies and manufactured news items. These negative imagery's are used to socially engineer a national consent that justifies attacking the group.

This same propaganda technique was used by Adolph Hitler to foster a nation consensual setting that allowed his heinous mistreatment of the Jews. Hitler's propaganda chief, Joseph Goebbels portrayed them as a fearsome enemy of German society through lies and manufactured news items. These negative imagery's were used to justify their annihilation.

In the case of African Americans, they are being portrayed as the face of degradation in the American society as to socially engineer consent for their mistreatment and facilitate their exploitation through the private prison industry– that earns immense profits through the disproportionately higher incarcerations and longer sentencing of African Americans. These private prisons now even hold stocks on Wall Street and their Board of Directors lobby for changes in the law that would increase their profits. The enhances sentencing drug laws and three strike felon laws are the results of these efforts. Moreover, it also stimulates the American economy by creating more jobs within the prison industry.
.

According to Dr Edward Bernays, one of America ’s most renowned propaganda specialists and consultant to many U.S. presidents; “This method of social manipulation is an important element in a democratic society, and that those who manipulate this unseen mechanism of society constitute an invisible government which is the true ruling power of our country.

The U.S. Government has an extensive history of conducting planned campaigns of extensive strategic psychological operations [based upon the works of Bernays] through the national media to influence and direct the perception and climate of the nation towards its governmental objectives. Given that the nineteen sixties were a period of massive black rebellion and unrest that eroded the American global image and increasingly placed the nation’s peace and stability in dire jeopardy and perhaps most particularly because the nations top sociologist and psychologist knew that those who make peaceful revolution impossible will make violent revolution inevitable. This quite logically necessitated that the U.S. Government employ these same pr oven methods of mass psychological manipulation against its entire African American population.
The U.S. Government now secretly deliberately disseminates false deplorably racially devaluing statistics and propaganda about its Black population that are deliberately designed to adversely manipulate and shape the minds and collective consciousness of its African American population– corrupting African Americans sense of unity, cohesion, and reason– and fostering a consensual national environment of where in which its Black population is more easily divided, exploited and ultimately suppressed. Given the white race’s unrivaled history and proclivity, for brutal racism, and greed of power, what else should have been expected, when they are in control of the media- the most powerful propaganda tool in the entire world.

When most people hear the term of psychological manipulation they usually think in terms of the classic “conspiracy theory” that refers to overt mind control such as mind altering drugs with carefully hypnotic programming. However, the real and true dangers are Bernays well proven methods of affecting the unconscious mind by using deception, and psychological manipulation. It is neither magical nor mystical, but a process that involves a set of basic social psychological principles. The constant relentless bombardment with deplorably negative images of themselves that of which African Americans are so inundated with, through a white controlled media, is a very carefully and deliberately designed psychological conditioning program. Its unrelenting daily assault on the Black psyche is designed to corrupt African Americans’ sense of racial unity and cohesion, mold the character of self-hatred, engender self-doubt, self-loathing, and distrust among their group. And while insinuating that Blacks admire, respect, and trust only Whites.
This method of psychological manipulation works by affecting the unconscious mind through deception. It uses the psychology of deceit to adversely affect the recipient group in terms of their behavior. Here is a simplified example of how this is being implemented against African Americans. Let us, for example, imagine that a crew of people was aboard their own massive ship and that this ship was being shadowed by another neighboring ship that was constantly broadcasting derogatory messages to the first group. Such messages as that their ship was lesser, smaller, not seaworthy, perhaps slowly sinking or that their crew was incompetent and was planning a mutiny. With time, the group receiving the negative messages, being unable to refute or to confirm these derogatory messages and deficiencies will grow weary and paranoid of the negative messages and will eventually comes to accept these negative assessments of themselves. The perception created by the taunting now unconsciously influences how the taunted group perceives themselves, subsequently causing them to become distrustful of themselves, doubting themselves, hating themselves and, eventually, fighting among themselves. The taunted group may even become so besieged by deep feelings of inadequacy that they may even jump into the sea and attempt to swim towards the taunting ship now believing it to be superior to their own ship even if their own ship was in fact better. The basis of this concept of mind manipulation is that the human being's most critical aspect is the mind and it works by affecting the mind through deception.
Within a real life setting this mortifying psychosocial treatment is precisely what is being deliberately done to African Americans through corporate owned and governmentally controlled media outlets that deliberately subjected them to seeing only the fraudulently worst in themselves. This is done through an immense campaign of false derogatory misinformation and false negative media reports and statistics that are created by U.S. governmental agencies and then leaked to its collaborators in the news media, which either knowingly or unknowingly carry the stories as their own. These false information about African Americans are then disseminated unrelentingly everywhere; it is deliberately perpetuated through news releases in magazine articles, radio, television, press releases, documentaries, and false census reports perpetuating and framing the myth of Whites’ racial, moral, and ethical superiority over its Black population. However, the weapon is not in how the message is carried, but is instead within the messages that it carries and how these messages detrimentally affects the Black population at large.
The over representation of Black crimes and grossly exaggerated statistics of Black on Black violence within this psychosocial program are intentionally designed to create fear, hatred, and distrust thus molding the character of disunity and self-hatred among the Black community. [Black’s own personal negative experiences and interactions with their fellow Blacks then merely confirm the program’s perpetuated message that it is they that are their own worst enemies]. The ultimately goal of this governmental psychosocial treatment of African Americans is to destroy the Black unity and cohesion that was historically the cornerstone of civil rights gains and that was a crucial factor of the survival of African Americans through more than four hundred years of racial oppression. [Logic dictates that given that unity and cohesion among African Americans was responsible for the demise of White America’s past system of blatant, institutionalized racism, then destroying this unity would be an essential objective of this psychological manipulation program.]

All African Americans have experienced the burden of this system of applied psychological conditioning, some more severely than others have. It is experienced every time we [Blacks] read a newspaper, watch the evening news, listen to a radio report, enter a classroom and read its racially biased textbooks. To the detriment of many African Americans, it has been an extremely effective. It has successfully conditioned many African Americans to accept the dominance of Whites and white institutions over their lives by misleading them to believe that they are, themselves, their own worst enemies, therefore engendering an aberration of internalized self contempt that pulverizes Black unity and halts Black upward mobility. It is at the root of both the profound division and self hatred now afflicting so many Black Americans and is at the heart of internalized feelings of superiority that many whites possess.
And while many African Americans have successfully navigated through this psychologically mortifying mine field and have gone on to lead successful, productive lives, for far too many this immense devaluation can seem inescapable and tragically, over time, many begin to accept subconsciously and painfully the negative portrayals of themselves. Many also become discouraged by the acceptance that their society is also preconditioned to see the worst in them and that, therefore, if they were ever to gain acceptance, if it is to be won at all, that success would be hard won. This in turn manifests negative internalized psychological pain and distress within many African Americans that can take many forms.
In fact, this governmental mortifying psychosocial treatment of African Americans may be the most aggravating, if not core, factor of the national phenomenon of self hatred; loss of educational aspirations; loss of unity, cohesion and racial pride; and fragile psyches of many African Americans today. It is in fact so fundamentally detrimental to the Black human condition and psyche that it may even affect the extent to which many African Americans realize their full human potential. This type of psychological manipulation program has also been proven very effective in rapidly destroying a group’s ethical and moral values and engendering negative cultural norms with regard to violence, brutality, and even murder. All people, to some degree, are products of cultural conditions and their worldviews operate outside of their level of consciousness. Therefore, no group can be preconditioned to see only the worst in themselves and not exhibit some degree of negative psychological impact.
Not only does this massive governmental psychological manipulation campaign negatively impacts Blacks self perceptions, but it also provides a more socially acceptable way to assure that the masses of African Americans remains the most racially devalued and most economical exploited and suppressed group in America. The media’s constant, fraudulently inaccurate, negative imagery of Black Americans is designed also to create a shift of victimization that changes the root problem of racism in America to be due to Black’s behavior rather than White’s proclivity for racism. Therefore insinuates that America would be a better society as a whole if African Americans were gone, thus engendering increasingly prejudiced distorted perceptions and acrimonious beliefs about African Americans that are designed to makes the nation and the entire world insensitive to their plight, tranquilizes efforts on their behalf, lessens pressure for social change on their behalf, and makes any serious criticism of White racism almost impossible today. Therefore fostering a national setting of where in which Blacks are more easily exploited and ultimately consensually suppressed. Moreover, some studies have shown that this shift of victimization now reflects increasingly acrimonious beliefs and prejudiced perceptions about and against African Americans that are arguably stronger today than they were after emancipation.
This campaign also attempts to discourage miscegenation between Blacks and whites, and creates a false justification for the legal system’s mistreatment of African Americans wherein they are disproportionately incarcerated, given stiffer sentences, and are more likely than other racial groups to be treated brutally, beaten, and fired upon by police officers while they are unarmed. These injustices now goes ignored because the perception has subconsciously become that it’s all now justified. When contempt of Blacks is made to appear to be justifiable, it is the fiercest and most effective type of racism because its witnesses, bystanders, and even world audiences will sit by idly allowing African Americans to be brutally mistreated under the belief that it is justified. This is what Dr. Edward Bernays referred to as “engineering consent”.

This governmental psychological conditioning program stripped African Americans of the national and international support that was acquired during the 1960's civil rights struggles. It also today affects attitudes that when enacted through governmental policies, laws, and other legislation actions, serve to ensure that African Americans will not advance. Its effects are manifested in ideas, education, governmental policies, economic stratification, social segregation, housing markets, hiring and promotion practices, psychological issues, and minority access to a variety of social services and opportunity.

The present despairing state of Black America is neither a baffling phenomenon nor the result of some divine ethnic curse, but is rather instead the result of the White elite’s innate proclivity for reinventing devious methods to suppress its Black population.
The objective of the United States government has always been to maintain its White dominance and control over its Black population, and clearly, psychological warfare meets this need. It was the logical choice because it covertly provided the U.S. Government with a far more sophisticated, proficient, and socially accepted means of covertly controlling and suppressing its Black population. Through this method the U.S. Government is able to both influence the national climate and engender personal psychological feelings among its Black population that meet its objectives of maintaining its white dominance. Furthermore, history overwhelmingly demonstrates that the White race’s innate proclivity for racism, control, and dominance is much too deeply ingrained for them to just merely give up their practices of implementing suppressive methods over its African American population. The records of history show that the reincarnation of suppressive methods into forms more acceptable to the changing times is a common practice of the United States government.
As seen after the abolishment of slavery wherein its methods of using racist, oppressive treatment of its Black population was reincarnated into Jim Crow inequalities that included many devious strategies and methods that prevented Blacks from becoming registered voters. And let us not forget the horrific Tuskegee experiments where of in which from1932 and 1972, the U.S. Public Health Service (PHS) conducted dangerous syphilis experiments on four hundred Black men. These men were deliberately left to degenerate painfully under the ravishes of the disease – with symptoms including blindness, tumors, paralysis, insanity and death – to allow the U.S. Government to collect the needed data from their autopsies. And let us also not forget of the CIA’s involvement in flooding the Black communities of Los Angeles with drugs and high powered weaponry and then disseminated these drugs and weaponry to many African American communities throughout the United States destroying the lives of millions of African Americans while stimulating the economy through the prison industry.

For more go to http://www.Divine Blacktruth.org and order the book entitled ” The Black Matrix: The Modern Mental and Social Suppression of African Americans Under National Interest. (c)2006, 2008

/ F. Jones
October 9, 2010, 4:39 am

Hey Chaz! I wish I was there to join your big Lost Party. How did it go? I must confess, like most of the show, The End was an unexpected surprise for me… I laughed, cried and learnt to let go with Jack. You are right, this was the best, smartest, best produced and most creative show I ever watched too. For me, this is “The Matrix” of modern television: the red pill gets you to live in the island where everything is possible and the blue pill is life outside the island, a world full of limitations.

/ Monica de Liz
November 12, 2010, 8:13 am