If I compute the SVD of a matrix A in Julia, it will give the sigma values of the matrix, BUT NOT in matrix form. However, if I want to assemble the sigma values of a matrix A into a diagonal matrix, is there any way to do this other than manually typing out the sigma values into the Diagonal() function?
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If I have to approximate the difference of norm of two matrices X and Y, it can be calculated through their eigen values by Mirsky's inequality .Now, I want to approximate the norm of difference of the eigen vector of the matrices, but I am stucked. Any help would be appreciated.
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.
I'm currently using BLAS function DSYMM to compute Y = AX and then DGEMM for YA', but I'm wondering is there some more efficient way of computing the matrix product AXAT, where A is an arbitrary n×n matrix and X is a symmetric n×n matrix?