# 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 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 ...
1answer
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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 ...
0answers
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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/...
2answers
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### 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 ...
1answer
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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 ...
1answer
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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? ...
0answers
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### Is FFT sub matrix degeneracy a problem in OFDM when there is noise in the frequency domain?

Say that the discrete Fourier transform (DFT) is used in OFDM. There are a number of degenerate (singular, non invertible) sub matrices of some DFT matrices. Does this result in any problems? One ...
1answer
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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 ...
1answer
445 views

### 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?
0answers
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### Implementing a beamforing algorithm for radar

I want to implement Real-time Radar Beamformer algorithm in C language, and the Conventional beamforming algorithm is as follow : ...
1answer
83 views

### 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 ...
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1answer
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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 (...
1answer
80 views

### 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 $CP$ ...
0answers
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### Calculate sampling lattice matrix in 2D

The pattern in which the sample points are distributed in 2 dims, is called a sampling lattice, and can be defined by a generator matrix.. In 2 dimensions, the generator matrix consists of 2 vectors. ...
3answers
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### Why do convolution kernels such as Gaussian, Laplacian, LoG almost always seem to be expressed in integers?

I'm a total newb in search of some deeper understanding, but I'm not able to read the maths behind these on Wikipedia. If I understand correctly, you get the new value for each pixel by multiplying ...
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606 views

### The rank of Fundamental Matrix

This question is regarding two view geometry where a point lying in the image plane of the first frame/ position of the camera is mapped onto the image plane of the second frame/ position of the ...
1answer
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### What is the difference between positive matrix coefficients and negative matrix coefficients of an audio?

I have turned an audio file into an one dimensional array by using audioread function in matlab and found several positive and negative fractional coefficient values.What is the basic difference of ...
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### A good reference for matrix completion [closed]

Does anyone know a complete reference or book on matrix completion?
1answer
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### Similarity or Relation between Walsh Hadamard Transform and Slant Transform

Is there any relation between Walsh Hadamard Transform and Slant Transform? Or is there any common property or similarity?
2answers
463 views

### Circular Convolution Matrix of ${H}^{H} {H}$

We all know that Discrete Fourier Transform (DFT) corresponds to circular (not linear) convolution. That is to say, if $x(n),h(n)$ and $y(n)$ is the original signal, the filter and output signal in ...
1answer
199 views

### Why discretize a continuous transition matrix in Kalman Filter?

In the Kalman filter toolbox at http://becs.aalto.fi/en/research/bayes/ekfukf/cwpa_demo.html the example code shows that a function lti_disc is called, which is essentially a matrix exponential ...
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2answers
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### What is the relation between kernel functions, kernels used in convolution and null spaces of a matrix?

I have recently started learning about machine learning and have come across kernels and null spaces. I understand that null space is the set of all vectors that satisfy the equation A.v = 0 (Where A ...