Lecture Note
University
California State UniversityCourse
MATH 150B | Calculus IIPages
1
Academic year
2023
Andrew Mathis
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0
p {margin: 0; padding: 0;} No Date 5) Inversion is tricky : (ABC) = C-B-4 6) Theorem : 4 A (mxn) and B (nxp) have inverse. then AB is invertible and (AB) = B "A" Proof : We have AA W In and A"A Im BB = In and B- B lp Thus, B - A (AB) B-KA-A) B= B "In B = Ip (11B) B'A = A (BB-1) 4 = A tn a's AA + c Im AB is invertible and (AB) = B-A" Transpose and Inverse 1) (AtB) = A'+B' 2) If A' = A, then A is called symmetric matrix Theorems: - Given two conformable matrices A and B, then (AB)' = B'A' - IF A is investible, then (A) (A)- (And A' is also invertible then (A) Properties of Symmetric Matrices If A' = A. then A is called symmetric matrix . If A and B are nxn symmetric matrices, then (AB) = BA If A and B are nxn symmetric matrices, then (A+B)'=B+A = if C is any nxn mathir then B=C'C is symmetric Useful symmetric matrices V = x'x P = x(xx)' X' m = 1-p = 1- X (x'x)-'x'
Transpose and Inverse
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