1
vote
1answer
31 views

Convolution composed with an invertible matrix

Let $T$ be an invertible $n \times n$ matrix and let $(h \circ T)(x)$ mean $h(Tx)$. Take functions $f,g$. Does it hold that $(f*g) \circ T = |det(T)| (f \circ T) * (g\circ T)?$ I have had some ...
3
votes
1answer
106 views

Which mathematical tool or method should I use to compare two matrices most efficiently?

I have two matrices(the first one is mxm, while the second one is nxn, m>n). They store data pertaining to human speech. The second matrix contains a data segment that acts like an acoustic ...
3
votes
0answers
234 views

Why matrix representation of convolution cannot explain the convolution theorem?

A record saying that Convolution Theorem is trivial since it is identical to the statement that convolution, as Toeplitz operator, has fourier eigenbasis and, therefore, is diagonal in it, has ...
0
votes
0answers
1k views

how does one convolve two matrices

so in OpenCV I retrieve a Gabor kernel for image processing which is a 10:10 matrix. I have a gray matrix of the original image. How do I convolve the two and get the output of the convolution? I'm ...
1
vote
1answer
539 views

a matrix inverse laplace transform problem

Let $\mathcal {L}^{-1}[\cdot]$ be an inverse Laplace transform. Let $A$ be a square matrix, and $I$ an identity matrix. Based on the fact that $\mathcal {L} ^{-1} [{(sI-A)}^{-1}] = e ^{tA}$, how can ...