Chapter 1.6 SpecialMatrices

Outline diagonal matrices triangular matrices

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Unformatted text preview: )T = (AT )−1 = A−1 . Outline Diagonal Matrices Triangular Matrices Symmetric Matrices Symmetric Products Theorem Suppose A = [aij ] is an m × n matrix. (a) AAT and AT A are symmetric matrices. (b) If A is invertible, then AAT and AT A are invertible. Proof. (a) (AAT )T = (AT )T AT = AAT and (AT A)T = AT (AT )T = AT A. (b) Since A is invertible, so is AT and therefore so are the products AAT and AT A. Outline Diagonal Matrices Triangular Matrices Example Example Demonstrate the Theorem using 1 2 −3 −4 2 A = 0 1 −1 −1 0 1 3 Symmetric Matrices...
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This note was uploaded on 02/10/2014 for the course MATH 2270 taught by Professor Kenyonj.platt during the Spring '14 term at Snow College.

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