- #1
jaejoon89
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Can somebody please explain to me when matrices commute? I've read that it's when they are diagonal with the same dimensions (and also scalar multiples?), but I don't understand why this is.
No, in most cases, matrix multiplication is not commutative. This means that the order in which matrices are multiplied matters and swapping the order of matrices will result in different products.
Yes, matrix multiplication is commutative when the matrices involved are scalar matrices (matrices with only one element) or when the matrices are equal.
Matrix multiplication is not commutative because the operation involves combining elements from two matrices in a specific order. This order matters because the position of each element in a matrix affects its value in the final product.
The general rule is that if the dimensions of the matrices do not match, then matrix multiplication is not commutative. However, it is always important to check each specific case to determine if the matrices are equal or scalar, which would result in commutativity.
Commutative matrix multiplication is significant in certain mathematical applications, such as linear algebra, where it allows for easier manipulation of equations and simplification of calculations. However, it is not a common property in most cases and should not be assumed without proper justification.