SOLUTION: Suppose A is a square matrix. Prove that there is a symmetric matrix B and a skew-symmetric matrix C such that A = B + C. In other words, any square matrix can be decomposed into a
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Question 1164529: Suppose A is a square matrix. Prove that there is a symmetric matrix B and a skew-symmetric matrix C such that A = B + C. In other words, any square matrix can be decomposed into a symmetric matrix and a skew-symmetric matrix (Proof Technique DC). Answer by ikleyn(52776) (Show Source):
For any square matrix A,
A = + . (1)
In this decomposition, is the matrix A "transposed".
In the decomposition (1), the matrix B = is s symmetric matrix, and the matrix C =
is the skew-symmetric matrix.
So (1) provides a required decomposition.
