# Questions tagged [matrix-decomposition]

Questions about matrix decompositions, such as the LU, Cholesky, SVD (Singular value decomposition) and eigenvalue-eigenvector decomposition.

1,441 questions
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### in Algorithms for Non-negative Matrix Factorization, the proofs of convergence, why is G(h,h') defined like this? [on hold]

because the auxiliary function has two different forms in this paper. h' has any special meaning? paper: Algorithms for Non-negative Matrix Factorization section: 6 Proofs of convergence Definition 1
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### Connection between SVD and Discrete Fourier Transform for Denoising

Denoising signals (in particular, 2D arrays, such as images) can be done by removing the high frequency components of the discrete Fourier transform (which is related to convolution with a Gaussian ...
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### Decomposition of 4x4 or larger affine transformation matrix to individual variables per degree of freedom

There are a couple of problems and solutions where affine matrices are decomposed into their separate transformations. However, they are all for the 2D case and I`m finding it difficult to generalise ...
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### Polar Decomposition of 2x2 Matrix

I have the following homework problem and I just don't know how to go about starting it. Is it asking me to find a unique value of ϕ? I just can't see any other solution apart from when ϕ = θ. So my ...
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### Understanding singular value decomposition example

I wanted to view SVD in action (using Octave) by running it on an image and then breaking it down into a set of rank 1 matrices. I'm getting stuck before that though, because I'm unable to reproduce ...
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### Solving an undetermined or overdetermined system of equations with constraints

I have a table that looks like this: I would like to determine the values for each of the different categories in the columns, such that col1*col2*col3 equal what'...
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### Why is the 'controllable subspace' actually controllable?

I am looking at the Kalman decomposition of a linear system into 'controllable' and 'uncontrollble' subspaces. The references I am using are these lecture notes and section 3.3 of 'Robust and Optimal ...
I have a question related to the Jordan-Chevalley Decomposition but I am also wondering about the general case. I have that V is a finite dimensional vector space over $\mathbb{C}$ and $T:V\... 2answers 3k views ### Block-diagonalizing an antisymmetric matrix I was wondering how to block-diagonalize a$10 \times 10$antisymmetric matrix into block matrices along the diagonal. Can I just diagonalize each non-diagonal block? Thanks! 2answers 80 views ### What do you call this equivalence relation?$A \simeq B$if$A = P^t BP$for some invertible matrix$P$If$A, B$are square matrices with coefficients in some ring, we say that$A$is similar to$B$if$A = PBP^{-1}$for some invertible matrix$P$. Similar matrices represent the same linear operator ... 1answer 24 views ### Representation of a matrix (tensor) Let us consider the following$2 \times 2$matrix,$A$. $$A = \begin{bmatrix} w_1^TP_{11}w_1 & w_1^TP_{12}w_2 \\ w_2^TP_{21}w_1 & w_2^TP_{22}w_2 \end{bmatrix}$$ where$P_{ij}$'s are$n\...
I am looking to find eigenvectors of circulant block matrices. I have a matrix given by: $$M= \begin{pmatrix}Z& A\\ B & Z \end{pmatrix}$$ where $Z$ is an $n\times n$ zero matrix, ...