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Solution: Exercises 22–26 provide a glimpse of some widely
Chapter 2, Problem 23E(choose chapter or problem)
Exercises 22–26 provide a glimpse of some widely used matrix factorizations, some of which are discussed later in the text.
(Rank Factorization) Suppose an \(m \times n\) matrix A admits a factorization A = CD where C is \(m \times 4\) and D is \(4 \times n\):
a. Show that A is the sum of four outer products. (See Section 2.4.)
b. Let m = 400 and n = 100: Explain why a computer programmer might prefer to store the data from A in the form of two matrices C and D.
Questions & Answers
QUESTION:
Exercises 22–26 provide a glimpse of some widely used matrix factorizations, some of which are discussed later in the text.
(Rank Factorization) Suppose an \(m \times n\) matrix A admits a factorization A = CD where C is \(m \times 4\) and D is \(4 \times n\):
a. Show that A is the sum of four outer products. (See Section 2.4.)
b. Let m = 400 and n = 100: Explain why a computer programmer might prefer to store the data from A in the form of two matrices C and D.
ANSWER:Solution 23E