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unchained1978

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- Thread starter unchained1978
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unchained1978

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Fredrik

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What do you mean by A*B and AB*. Are A and B complex numbers, n×1 matrices, or something else? If they are n×1 matrices, then <A,B>=AB* doesn't work, since the right-hand side is an n×n matrix. (Note that A* and B* are 1×n matrices). But you could define <A,B>=B*A if you want to.

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unchained1978

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Fredrik

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If the vector space is the set of functions from a set X into ℂ, then <f,g>=f*g isn't an inner product, since f*g is a function, not a member of ℂ. (The "complex conjugate" of a function is defined by f*(x)=f(x)* for all x, and the product of two functions is defined by (fg)(x)=f(x)g(x) for all x, so f*g is the function that takes x to f(x)*g(x)).

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