# Tag Info

Accepted

### 2D Convolution as a Doubly Block Circulant Matrix Operating on a Vector

The point is that circular convolution of two 1-D discrete signals can be expressed as the product of a circulant matrix and the vector representation of the other signal. The circulant matrix is a ...
• 4,105
Accepted

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

If $H$ is a matrix form of Circular Convolution then it is a Circulant Matrix. Being a Circulant Matrix means it can be diagonalized by the Fourier Matrix ${F}$: $$H = {F}^{H} D F$$ Where the ...
• 41.2k
Accepted

### Least Angle Regression (LARS) without Matrix Inversion

If you want to solve for single value of $\lambda$ in the model: $$\arg \min_{x} \frac{1}{2} {\left\| A x - b \right\|}_{2}^{2} + \lambda {\left\| x \right\|}_{1}$$ Then you can use Coordinate ...
• 41.2k
Accepted

• 31

### why use svd() to invert a matrix?

The two methods differ, above all, by their applicability to matrix classes. col (cholesky) decomposes Hermitian, positive-definite rectangular matrices into the ...
• 1,415
Accepted

### Proving that the uncertainty can not increase during the update step of a Kalman filter - positive semidefiniteness

$Q_t$ is real-valued and positive definite, thus $Q_t^{-1}$ is real-valued and positive definite. Now it's just making up a lemma of the Cholesky decomposition: If $Q_t^{-1}$ is real-valued and ...
• 8,610
Accepted

### What is the complexity of multiplication a real matrix with real vector

If you multiply an $M \times N$ matrix with an $N \times 1$ vector you get a vector of size $M \times 1$ For the generic case you will need $M \cdot N$ multiplications and $M \cdot (N-1)$ additions. ...
• 32.5k

### Analytical expression for the eigenvectors of a 3x3 real, symmetric matrix?

There's a newer (2017) closed-form formulation for the eigendecomposition of 2x2 and 3x3 Hermitian matrices here: Charles-Alban Deledalle, Loic Denis, Sonia Tabti, Florence Tupin. Closed-form ...
Accepted

### Difference Between Correlation / Convolution and Matrix Multiplication

Well I will try to explain. Let us first discission in time domain: 1) Let us say you have two signals, x and y. By Convolution in time domain, you mean that you flip(invert) one of the signals(lets ...
• 116
Accepted

### How is the sound converted to matrix in Matlab?

The function audioread doesn't generate any values, it just reads audio samples stored in a file. If you want to generate the sound of a guitar, you need to look ...
• 80.4k

### 5.1 Rear To 5.1 Side mixing matrix

The commonly called 5.1 format uses only surround channels, which are defined as rear/side channels in ITU-R BS 775. The case you want to deal with (turning rear surround channels to side surround ...
• 277
Accepted

### Mechanics of a matrix Interleaver

We have different interleaving techniques, and matrix interleaving is one of them. But at the end all of them do one thing: interleaving is a technique to protect against burst errors (no matter how ...
• 4,105
Let me take a stab at it. You agree that $\mathbf{R}_k$ is positive definite. Since it is the variance. Now, $\mathbf{P}_{k|k-1}$ is also positive definite as it is a covariance matrix, as ...