Question

prove that "any square matrix is equal to sum of symmetric and skew symmetric matrix
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Answer 1

Answer:

Prove that

C=12(C+CT)+12(C−CT)

What I have manage so far is:

a. Let S be a Symmetric Matrix so S=C+CT

b. Let N be a Skew-Symmetric Matrix so N=C−CT

Proof:

St=[C+CT]T=CT+C=S

Nt=[C−CT]T=−CT+C=−N