8. Robinsonian reordering of symmetric square matrices: use the given square matrix as a
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Let Cn×n be a square matrix.
Prove thatC=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
Prove thatC=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
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