Solved: In the text we defined a matrix A to be symmetric if AT = A. Analogously, a

Chapter 1, Problem 44

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In the text we defined a matrix A to be symmetric if AT = A. Analogously, a matrix A is said to be skew-symmetric if AT = A. Exercises 4145 are concerned with matrices of this type.Prove that every square matrix A can be expressed as the sum of a symmetric matrix and a skew-symmetric matrix. [Hint: Note the identity A = 1 2 (A + AT ) + 1 2 (A AT ).]

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