# Questions tagged [matrix]

is a mathematical object to be recorded in a [usually] rectangular array of elements of ring or field, which (table) is a set of rows and columns are located at the intersection of its elements. The number of rows and columns specify the size of the matrix.

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### Optimization Problem in Graph Signal Processing to find edge weights

I am working on an application which consists of cross-roads and roads that connects them. In my design, I am using graph signal processing to estimate the importance of the roads which means edge ...
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### What is the complexity of big-$O$ $O(N \times \mathrm{log}_2(N))$ vs real operations

I usually see books/references writing the complexity of such operations as $O(N \times \mathrm{log}_2(N))$; For example, the complexity of FFT/IFFT operation is $O(N \times \mathrm{log}_2(N))$. ...
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### How can I explain the result of of multiplications by matrices

I have a vector $x$ with size $N \times 1$, it's multiplied with a $Z$ matrix $N \times N$, the resulted $N \times 1$ vector is $y = Zx$. I know that each value of $y_i$, where $i = 0, 1, 2, .., N-1$ ...
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### Expressing mathematically the number of real addition operation for a vector after dividing it

I assume I have the length of such vector $y$ is $N$. In the first time I divide that vector into two columns and then sum them point-wise summation. The second time, I divide the same vector $y$ ...
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### Converting 2 variables (obtained by ICA decomposition) named A_ffdiag and W_ffdiag into mixing/unmixing matrix

I have two variables as a result of an ICA (Independent Component analysis) decomposition (decomposed using joint diagonalization algorithm which uses frobenius norm formulation) named A_ffdiag and ...
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### Signal Processing on non-Euclidean domains

I have a very simple yet fundamental question. Suppose I have a vector of data $x \in \mathbb{R}^N$. Without additional information, I guess the majority of people think this vector as defined over ...
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### Proving that the uncertainty can not increase during the update step of a Kalman filter - positive semidefiniteness

I am trying to prove mathematically that the update step in a Kalman filter can not result in a increase in uncertainty. I found the following proof which is based on the inversion lemma and the ...
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### how do you know if your matrix is sparse after sparsifying transform?

To successfully compress the data using Compressive Sensing method, I need to have sparse vector, theoretically a vector is sparse if the entries of the vector has many zero or nearly zero. My ...
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### Relation between the matrix trace and the amplitude of each element

Assume a diagonal matrix $\mathbf X$ whose size $N\times N$ and its diagonal elements are $0.5 + 0.5i$, and the vector $\mathbf p$ of size $N\times 1$ whose elements have similar amplitude. I have ...
981 views

### linear convolution toeplitz matrix vs circular convolution toeplitz matrix

I have an issue in understanding the difference between building the Toeplitz matrix when the convolution is linear and when it's circular. As I know that Toeplitz matrix $H$ can be built as following ...
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### Stability of $x(n) = A x(n-1)+b$

I am looking at the following system: $x(n) = A x(n-1) + b$ where x and b are vectors and A is a matrix. How can I derive the stability and causality conditions for such a system using Z transform? If ...
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