this post was submitted on 15 Mar 2025
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Could one of you scholars please explain the joke for us smoothbrains who don't get it? All I see is a boolean matrix, and I'm not even sure that is correct.
A square matrix with the ones in the diagonal is called the identity matrix
It's an identity matrix. You multiple a vector with it and the result is still the same (identical) vector
That matrix of zeros with one in diagonal is called the matrix of identity.
It is famous because when doing multiplication on matrix or vector, it acts likes 1 on "normal" number:
x times 1 is x anyMatrix times Identity is anyMatrix.
Wouldn't you need to put
anyMatrixfirst, since matrix multiplication isn't commutative?You are right. I will correct it.
No I just tried it and I was wrong, it seems like it doesn't matter for the ID matrix specifically
I need to freshen up on my linear algebra. I don't remember on which sense it goes but I think if you swap the factors, you'll have to you transpose the matrix x to keep the same result.
Huh? Identity times anyMatrix is also anyMatrix. The matrix just has to have the right dimensions
Eigen see how this is confusing, I don't get it either
You multiply vectors and matrizes row by column.
So for any matrix the fitting identity matrix multiplies each row on the relevant position by one and puts it into a column.
The matrix remains the same.
See example 5 here: https://www.geeksforgeeks.org/identity-matrix/
It's like if you multiply or divide by one. Just a bit bigger cuz linear algebra.