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Topics in Matrix Analysis by Charles R. Johnson, Roger A. Horn

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Chapter 6

Matrices and functions

6.0    Introduction

If A is a matrix and f(·) is a function, what could be meant by f(A)? There are many interesting examples of functions f: Mm,nMp,q, depending on the values of m, n, p, and q and the nature of the functional relationship. Familiar examples of such functions are tr A and det A (if m = n), vec A, A → AA* (p = q = m), A → A* A (p = q = n), A → the kth compound of image, AAB (B image Mr, s’ p = mr, q = ns), Af(A) (f(·) a polynomial, p = q = m = n), A → A A (p = m, q = n).

    If m = n = 1, we have ...

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