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Properties of Matrix Multiplication
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We state the properties of matrix multiplication relative to addition and scalar multiplication. With these operations the standard commutativity and associativity hold. We show by example that matrix multiplication is not commutative in general, and also show that nilpotent matrices exist.
We prove that the transpose of a product is the product of the transposes in reverse order: (AB)^T = B^T A^T.
#mikethemathematician, #mikedabkowski, #profdabkowski
We prove that the transpose of a product is the product of the transposes in reverse order: (AB)^T = B^T A^T.
#mikethemathematician, #mikedabkowski, #profdabkowski