expected symmetric matrix
Why is the resulting matrix not symmetrical?
Jim
Hand multiplication gives a matrix that is not symmetrical
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I want to create an orthogonal symmetric matrix of size 5 and size 6. Is there a way for me to generate this type of matrix? An orthogonal symmetric matrix is when a matrix A is equal to its transpose and also its inverse.
I've tried searching for ways to do this but all I get is how to generate an orthogonal matrix or how to generate a symmetric matrix. Couldn't find a way to generate an orthogonal symmetric matrix.
I know that the mse between two 2d matrices, A and B, of shapes pxq, can be calculated in matrix terms as follows:
1/n tr(AtB)
The nice thing about this equation is that the matrices At and B are conformal to matrix multiplication and also yields a square matrix which has a defined trace.
But if we have two 3d tensors A and B of shapes pxqxr, then I don't understand how to get the outer product between them to get a square matrix so that the mse camne written in terms of trace.
When I perform QR decomposition on a 3x2 matrix A in Julia, it gives a 3x3 matrix Q. Is there any way I can get a "thin" version of this QR, where it returns a Q that is 3x2 (same dimensions as matrix A)? My goal is just to get an orthonormal basis for the column space of A, so I don't need a 3x3 matrix Q.
This can be achieved with Matrix(qr(A)). qr doesn't return matrices, but rather returns an object that can multiply by other matrices or easily extract the thin or full Q matrix.
Discr. convolution can be represented as multiplication of input with matrix M.
Where M is presented a special case of Toeplitz matrices - circulant matrices.
The questions is: is 2d convolution can also be represented as matrix multiplication?
p.s. By dicr. convolution I mean dicr. convolution with indexing discrete samples in modulus fashion, i.e. the discrete signal is repeating
....X[n-1]x[0]x[1]...x[N-1]x[0]...
Yes, it can, but it will generally be a rather big matrix. If your data set is on a grid of size NxM, then the convolution is a matrix operating on a vector of length N*M; the convolution matrix has N2M2 elements.
If your convolution kernel is small, then the matrix will typically a band matrix where the width of the band is at least N or M.
How can we find inverse of a matrix using Simplex method? Do we need to have square matrix only or inverse can be found of any matrix? Also specify about the upper bound on the matrix size?
The Matrix Inverse is required during simplex only over the Basis Matrix (Basis Inversion).
Base matrix is a square matrix of dimensions (mxm) where m is the total number of constraints.
This Matrix Inversion is carried out using either the Product form of Inverse or LU Decomposition.