If we consider the vectori space of all square matrix on a certain field K, all the matrices that are antisymmetrical form a subspace of that. I have to rove this statement, but I have a problem. The identity matrix is obviously not antisymmetric, so I cannot find an identity element for the vector space... and also the rest of the statement appears rather obscure to me...
Antisymmetric matrix space
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linear-algebra
matrices
1 Answers
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I think you're confusing what the identity elements are. For the vector space of matrices the operation is just matrix addition so the identity element is the matrix with all zero entries. This is antisymmetric.
The identity element for matrix multipication is not antisymmetric, as you pointed out.