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Question
Submitted by infinitythomas on Fri, 2012-05-11 13:07
due on Tue, 2012-05-15 13:06
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Physics directed to mathematician

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Answer
Submitted by mathematician on Fri, 2012-05-11 13:09
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Solutions (Credit goes to George Jackson)

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The xxxxxxxxxxxx xx x square matrix are the non-zero vectors xxxxx xxxxx being xxxxxxxxxx by the xxxxxxx remain xxxxxxxx to xxx xxxxxxxx vector. For each xxxxxxxxxxxx xxx xxxxxxxxxxxxx eigenvalue xx xxx factor by xxxxx the xxxxxxxxxxx xx scaled when multiplied by the xxxxxxx xxx xxxxxx eigen- xx xxxxxxx from xxx xxxxxx word "eigen" for xxxxxxxx xx the xxxxx of a characteristic description. The xxxxxxxxxxxx xxx xxxxxxxxx also xxxxxx xxxxxxxxxxxxxx xxxxxxxx xxxxxxxxxx the xxxxxxxxxxx xxx xxxx known as xxxxxxxxxxxxxx xxxxxxx

xxx mathematical xxxxxxxxxx xx xxxx xxxx is as xxxxxxxx if x xx a xxxxxx matrix, a xxxxxxxx xxxxxx x is xx eigenvector of A xx xxxxx is a xxxxxx xx (lambda) such that

xxx scalar λ xxxxxxxx xx said to xx the eigenvalue of A corresponding to xx An eigenspace of A is the xxx of all xxxxxxxxxxxx xxxx xxx xxxx xxxxxxxxxx together with xxx zero vector. However, xxx xxxx vector xx xxx an xxxxxxxxxxxxxxx

These xxxxx are xxxxx extended xx more xxxxxxx xxxxxxxxxxx where

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