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unscientific
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Homework Statement
Let V be the real vector space of all real symmetric n × n matrices and define the scalar product of two matrices A, B by (Tr (A) denotes the trace of A)
Show that this indeed fulfils the requirements on a scalar product.
Homework Equations
Conditions for a scalar product:
The Attempt at a Solution
I'm not sure how to show the last part. Which can be summarized as:
<A|B> = 0 if ATA = I and BTB = I
The first 3 parts of my attempt are shown below: