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lecture9 - Lecture 9 Symmetric Matrices Subspaces and...

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Lecture 9 Symmetric Matrices Subspaces and Nullspaces Shang-Hua Teng

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Matrix Transpose Addition: A+B Multiplication: AB Inverse: A -1 Transpose : A -T ( 29 ji ij A A =
Transpose = 8 4 7 3 6 2 5 1 8 7 6 5 4 3 2 1 T [ ] = 5 4 3 2 1 5 4 3 2 1 T

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Inner Product and Outer Product [ ] 70 32 21 12 5 8 7 6 5 4 3 2 1 = + + + = [ ] = 32 24 16 8 28 21 14 7 24 18 12 6 20 15 10 5 4 3 2 1 8 7 6 5
Properties of Transpose ( 29 ( 29 ( 29 ( 29 1 1 - - = = + = + T T T T T T T T A A A B AB B A B A End of Page 109: for a transparent proof

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Ellipses and Ellipsoids 1 2 2 = + r y R x [ ] 1 / 1 0 0 / 1 , = y x r R y x R r 0 [ ] 1 / 1 0 0 0 0 / 1 1 1 1 = n n n x x r r x x
Later R r 0 ( 29 y A x y Ax T T T = Relating to

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This note was uploaded on 03/08/2010 for the course CS 232 taught by Professor Bera during the Spring '09 term at BU.

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lecture9 - Lecture 9 Symmetric Matrices Subspaces and...

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