The Frobenius inner product is defined as ?A, B? = trace(AB?). for n × n matrices A and B. Verify that ?A, B? defines an inner product on M???.
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Conjugate Symmetry: For any two matrices A and B, we have (A, B) = trace(AB^T) = trace((B^TA^T)^T) = trace(B^TA) = (B, A). So, the Frobenius inner product is conjugate symmetric. Show more…
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