All Questions
Tagged with matrix-decomposition matlab
41
questions
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Matlab qz algorithm not reliable
I programmed my own version of the qz algorithm and, while testing it's results using the matlab qz algorithm, I found a particular case where my solution reaches an upper-triangular matrix and matlab ...
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47
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How can I compute the null vector using QR factorization?
Assume that you have a matrix $X$ and you want to compute the complex eigenvectors. You only know the complex eigenvalues.
With that information, you could solve the null space formula $$(A-\lambda I)...
- 2,962
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358
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MATLAB Code Help. Using Crout's Method, solve the system of linear equation $Mz=f$, where $M=\begin{pmatrix}I &A\\A^T&0\end{pmatrix}$
Using Crout's Method, solve the system of linear equation $Mz=f$, where $$M=\begin{pmatrix}I &A\\A^T&0\end{pmatrix}$$
I have implemented algorithm of Crout's method. But I don't have any idea ...
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The magic behind MATLAB's powerful matrix decomposition algorithms [closed]
I have always wondered how MATLAB's built-in function for matrix decomposition are crafted and optimized. Examples of MATLAB's built-in function for matrix decompositions are $\mathsf{qr},\mathsf{svd},...
- 179
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504
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vandermonde decomposition of a Hankel matrix
Suppose, I have a Hankel matrix H of rank-K and size L x M, I want to decompose H into vandermonde decomposition as:
\begin{equation}
H = SCT^T
\end{equation}
where S and T are vandermonde matrices of ...
- 57
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37
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Problems with eigendecomposition of a big stochastic matrix
I face the following problem. I generate a big $1202 \times 1202$ stochastic matrix $Q$ whose columns adds to $1$ (up to numeric precision). The elements of $Q$ are in $[0,1]$. I use the ...
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How to get eigenvectors using QR algorithm?
From everything I've heard, this matlab code ought to spit out a matrix where each row is the same. So why doesn't it?
...
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given a symmetric matrix $A_{n\times n}$ and integer $m$, is there any matrix $X_{n\times m}$, s.t., $X\times X^{t}=A$?
Recently I've come across the following problem. I would be very pleased if someone helps me how to deal with.
given a symmetric matrix $A_{n\times n}$($n$ is fixed) and positive integer $m$, is there ...
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88
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Can we decompose an array of algebraic expressions into a product of matrices that separate known variables from unknowns?
Given vectors $\sigma, \tau \in \Bbb R^n \ge0$, and constant $\mu \in \Bbb R^1>0$, let matrix-valued function $C : \Bbb R \to \Bbb R^{2 \times n}$ be defined by $$C (\mu) := \begin{bmatrix} \vec\...
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290
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How to prove that elements in the main diagonal of PD matrix are all positive?
Reminder: As PD matrices are defined vector X is not the vector 0
Given a positive definite matrix A which is symmetric
We need to prove that he following elements in the main diagonal are all ...
- 131
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2
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66
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The number of operations to multiply L by U?
I have the following $A=LU$
while $L$ is is lower triangular matrix and $U$ is an upper triangular matrix, the size of both $L$ and $U$ is $N\times N$.
The question is how many operations are ...
- 131
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140
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How to ensure a positive definite covariance matrix?
I'm trying to model correlated noise by defining a covariance matrix and multiplying the Cholesky decomposition of it by a vector containing uncorrelated noise. How can I ensure the covariance matrix ...
- 11
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646
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Smith normal form of rectangular matrix in MATLAB
Suppose I've got a nonsquare integer matrix, say $\begin{pmatrix}3 & 1 & 1 & 1\\1 & 1 & 1 &1\end{pmatrix}$ and want to compute its Smith normal form--in this case, $\begin{...
- 485
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409
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Is there way to simplify or improve efficiency of LU factorization algorithm?
I have attempted to implement LU facotorization from pages 3-6 of this document:
http://www4.ncsu.edu/~kksivara/ma505/handouts/lu-pivot.pdf
An example of running the code below for a simple 4x4 ...
- 1,355
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Matlab Code-Include Iteration to QR Algorithm Gram-Schmidt - The Iterations of A will converge to Eigenvalues
Still need to add the iteration to the Matlab Code of the QR Algorithm using Gram-Schmidt to iterate until convergence as follows:
I am having trouble completing the code to be able to iterate the ...
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