Question

Express every Square Matrix is a sum
of Symmetric and Skew - Symmetric
matric​

Answer 1

Answer:

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Step-by-step explanation:

Any Square matrix can be expressed as the sum of a symmetric and a skew-symmetric matrix. Proof: Let A be a square matrix then, we can write A = 1/2 (A + A′) + 1/2 (A − A′). From the Theorem 1, we know that (A + A′) is a symmetric matrix and (A – A′) is a skew-symmetric matrix.

Answer 2

• Given A be a square matrix.
• Now A can be written as,
• Claim, B is symmetric and C is skew-symmetric.
• BT =21(AT+(AT)T)
• So B is a symmetric matrix.

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