# Questions tagged [linear-algebra]

is a branch of algebra, concerning linear nature of objects: vector or vector spaces, linear transformations, systems of linear equations, quadratic and bi-linear forms, among the main tools used in linear algebra is the determinants of the matrix pair. The theory of invariants and tensor calculus is usually considered as integral parts of linear algebra.

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### Proving that a product of matrices invertible

Given $R_x$ a Positive Definite (PD) covariance matrix of size $M\times M$ and $C$ a full rank $M \times N$ matrix, I want to prove that $C^* R_x^{-1} C$ is invertible to derive the Linearly ...
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### Orthogonal Basis for a 2D Signals (Compressive Sensing)

I have a 2-D signal that is (1536x128) and that is sparse in the Fourier domain (after applying fft2). I want to apply compressive sensing to recover the signal using fewer random elements, but I am ...
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### Linear Systems, Sparse Solutions, and $4 \times 4$ Sudoku Algorithm [closed]

I am unable to understand the paper Linear Systems, Sparse Solutions, and Sudoku. I have to form a $4 \times 4$ Sudoku using the algorithm in this paper. Can somebody please provide me the algorithm ...
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### Help with Determinants [closed]

Okay so i understand the first det, which is why i got the correct solution. However for the second det, im not sure how to solve it since because of the different coefficents (0,2,4) and i tried of ...
427 views

### Deriving Frequency Response for 2-pole Zero-Delay Feedback State Variable Filter

I have an existing zero-delay feedback (ZDF) 2-pole state variable filter implementation (along the lines of the theory presented in VA Filter Design by V. Zavalishin), and I wish to determine the ...
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### Restriction of Fourier Transform

I am currently reading Candes et. al.'s 2006 paper on recovery of sparse signals from incomplete frequency samples. I am having trouble figuring out what is the form of the Fourier transform ...
1k views

### Sensing matrix for compressed sensing

What are the differences between random binary sensing matrix  and random Gaussian sensing matrix? What the advantages and disadvantages of each matrix? How can I choose the suitable matrix for a ...
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### Proof of complex conjugate symmetry property of DFT

According to the Proof : \begin{align} X_n &= \sum_{k=0}^{N-1}x_ke^{-j\frac{2\pi k n}{N}}\\ X_{N-n} &= \sum_{k=0}^{N-1}x_ke^{-j\frac{2\pi k (N-n)}{N}}\\ &=\sum_{k=0}^{N-1}x_k e^{-j 2\pi ...
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### What are the practical constraints on designing Sensing matrix in compressed Sensing?

In a typical compressed sensing scenario, $y=Ax$, where $x$ is a sparse signal and $A$ is the sensing matrix. To reconstruct the sparse signal $x$ from $y$, $A$ should posses the Restricted Isometry ...
515 views

### Alternative to Orthogonal Matching Pursuit (OMP) Algorithm

In the Compressed Sensing context, assume there is a signal $x \in {\mathbb{R}}^{n}$ which is $k$ sparse. Namely its Pseudo ${\ell}_{0}$ Norm is ${\left\| x \right\|}_{0} = k$ (The signal has ...
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### How to find out if a transform matrix is separable?

In image processing, when we have a series of basis images, how could we know if the transformation is separable or not? For example, I know that following bases are separable and transformation can ...
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### Deriving the Matrix Inversion Lemma for RLS Equations vs the Woodbury Derivation

Can any one help me in deriving the matrix inversion lemma rule for RLS algorithm? I don't know how to start with. Many books have just stated but they haven't derived it.