Transpose and Inverse | California State University, Northridge - Edubirdie

University:
California State University, Northridge
Course:
MATH 150B | Calculus II
Academic year:

2023
Views:

320

Pages:

1
Author:

Andrew M.

5) Inversion is tricky (ABC) CBA 6) Theorem & A (mxn) and B (nxp) have inverse. then AB is invertible and (AB) BA Proof1 We have and AA Thus, BA" (AB) BYAA) 661.888 (15) B4"(68) 4 ALA AA AB is invertible and (AB) 6"A" Transpose and Invese 1) (A+B)=A+B 2) If A' A, then A is called symmetrie matrix Theorems: Given two conformable matricas A and B. then (AB) B'A' If A is invertible, then (A') = (A') (And A' is also invertible, then (A) Properties of Symmetric Matrices If A' A, then A is called symmetric matin • If A and B are nxn symmetic matrices, then (AB) = BA It A and & are non symmetric matrices, ther (A+B) =B+A • If C is any nan matur, then B-CC is symmetric → Useful symmetic matrices x'x p = x(xx) x M = 1-p= 1-x (xx)

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