Exercises 22–26 provide a glimpse of some widely used matrix factorizations, some of which are discussed later in the text.
(Singular Value Decomposition) Suppose A = UDVT, where U and V are n × n matrices with the property that UT U = I and VT V = I , and where = is a diagonal matrix with positive numbers σ1,…, σn on the diagonal. Show that A is invertible, and find a formula for A–1.
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