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.
 Spring '14
 KenyonJ.Platt
 Linear Algebra, Algebra, Matrices

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