# 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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### 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 to find significance of time varying regression coefficents in a regression model? ex student-t

I am in a requirement of finding the significance of time varying coefficent b(t) in the below multi linear regression model: $$y(t) = a(t)x_1(t)+b(t)x_2(t).$$ I have looked into student-t test to ...
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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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### Can I reduce the complexity of Fourier transform and equalization into one matrix multiplication

I have a signal $x \in \mathbb{R} ^{N \times 1}$, I need to perform Fourier transform, then zeros forcing equalizer (which means wise-element division by constant) and then inverse Fourier transform....
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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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### Multiplication of Fourier repeated matrix with a higher dimensional matrix

I have a square Fourier matrix $F_{2\times 2}$ with size of $2 \times 2$. It’s repeated twice following this way: $F_r = F \bigotimes I_{2 \times 2}$, where $\bigotimes$ is the Kronecker tensor ...
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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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• 640
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### Can we recover a vector from one element of resulted vector after multiplication?

I have a matrix $X = \begin{bmatrix} 0.5000 + 0.5000i & 0.5000 - 0.5000i\\ 0.5000 - 0.5000i & 0.5000 + 0.5000i \end{bmatrix}$ multiplied with a column containing a complex number and its ...
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### Camera Calibration: Intuition for the extrensic parameters in relation to the camera center and intrinsic parameters

In our lecture we have learnt that the extrinsic parameters would transfer a point $X_\text{World}$ described in world coordinates to a point $X_\text{cam}$ in camera-coordinates In in-homogeneous ...
1 vote
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### Estimating Correlation Matrices

I am trying to obtain the correlation matrices of two random signals. Both of them, $X$ and $Y$, are white Gaussian Noise, with unitary variance. However, they are correlated, with correlation ...
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### Matrix multiplication computational complexity based on radix 2

I am wondering, can we use Radix 2 based computational-complexity calculation for any matrix multiplication whose size is $N$ x $N$ ?? where $N$ = $2^K$ and $K > 1$ is an integer ?? Or it can only ...
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1 vote
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### Optimization of square matrix multiplied with another matrix to have the final result a unitary matrix

I have a square matrix $D$ whose size is $m \times m$ multiplied with another $m \times m$ square matrix $C$, I need to optimize the matrix $C$ to have a unitary matrix $DC$. I mean optimize the ...
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### Wave Digital Filter Bridge-T Resonator implementation, gives expected cutoff frequency but incorrect gain and roll-off

Trying to implement the WDF in Fig 5(a) of this publication. The response of the ideal op-amp implementation is given by the black curve in Fig 7: Here is the plot I get when trying to implement the ...
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### What is an analysis dictionary or operator in compressive sensing?

I am doing research on compressive sensing. I am new in this field. I read several papers regarding analysis dictionaries. Here are some papers that I have read so far: https://www.hindawi.com/...
186 views

### Why do we need to estimate eigenvalues?

I am not working in signal processing field, but recently I happen to read a paper which estimates source numbers using Gerschgorin radii, and I feel kind of confused about why we need to estimate ...
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1 vote
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### Matrices of complex numbers multiplication

I'm trying to implement the multiplication of two matrices something like this picture in c langage. I want to read the numbers from a text file of x and store it later in an array the code that i ...
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1 vote
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### What is the relation between eigenvalues and state-space response in control systems?

I understand the mathematics behind it but I want to know what happens physically in a real-life system. How do the eigenvalues come into the picture from a non-mathematical (physical) point of view? ...
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### Is FFT sub matrix degeneracy a problem in OFDMA for some type of noise?

Say that the discrete Fourier transform (DFT) is used in OFDMA. There are a number of degenerate (singular, non invertible) sub matrices of some DFT matrices. Does this result in any problems? One ...
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### Property of the trace and expectation

I'm reading the paper Model-Driven Deep Learning for Joint MIMO Channel Estimation and Signal Detection by Hengtao He, Chao-Kai Wen, Shi Jin, and Geoffrey Ye Li on Orthogonal Approximate Message ...
1 vote
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### why use svd() to invert a matrix?

In MATLAB, i compared elapsed time to invert a Hermitian matrix using inverse(), svd(), and chol(). svd() took the longest. So is there any reason to prefer svd() to the other two methods?
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### How can I find expansion coefficients of the a vector in a given basis?

How can I find the coefficient of the vector $\mathbf y$? And how can the inner product be done on these vectors? Let $\mathbf y = \begin{bmatrix}1\\2\\0\\1\end{bmatrix}$ What are the expansion ...
1 vote
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### On the use of Permutation matrix to perform iFFT

I have a question about using the permutation matrix for performing $iFFT$ for such matrix and then reshape it row-wise and column-wise way. Let's say that we have a random matrix $x$ whose size is (...
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### Effect of Adding the cyclic prefix on the toeplitz matrix in OFDM

Assuming we have $N$ symbols to transmit encoded in block $k$, Performing $N$−iFFT at the transmitter, we now have The resulted signal $x(k)$ has length of $N$. inserting a cyclic prefix $CP$ ...
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