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Show that every square matrix can be uniquely expressed as a sum of symmetric and skew symmetric matrix.
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written 7.9 years ago by
teamques10
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• modified 7.9 years ago |
Let, A be any square matrix.
Now, $ A = \dfrac{1}{2} (A+A') + \dfrac{1}{2} (A-A') \; = \; say, \; P+Q \; where \\ \; \\ P=\dfrac{1}{2} (A+A') \; \; and \; \; Q=\dfrac{1}{2} (A-A') \\ \; \\ To \; prove: \; P \; is \; symmetric, \; i.e. \; …
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