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 ...

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Using a Wiener Filter to Estimate a Transfer Function

As a follow-on to this question about estimating a transfer function of an unknown system using a Wiener filter, How would you put a minimum MSE criteria on how well the estimated filter weights ...
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117 views

Estimate the transfer function of an unknown system?

Suppose you have a system, H, that you want to estimate its transfer function. You have a finite number of complex input samples, x, and noisy complex (magnitude and phase) output samples, y: In ...
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Relationship between Discrete Deconvolution and Toeplitz Matrices

I have 2 vectors, $a$ & $c$, both of length M. I know they are related by $a*b=c$. My goal is to recover $b$. Obviously $b=$deconv$(c,a)$. I am only interested in the first M elements of the ...
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How to understand relationships between ellipse and second moment matrix of Harris corner detector?

guys. I am really lacking in knowledge of linear algebra. I am reading slides of Harris corner. But I am really confused about one of them. I know that I can find corners by two large eigenvalues but ...
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Calculate the entropy of Turkish alphabet and compare with the entropy of English alphabet with using Matlab?

Calculate the entropy of Turkish alphabet and compare with the entropy of English alphabet with using Matlab? How can ı do this question anybody help please?..
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What are the mathematical consequences of a discrete signal living in Hilbert space?

I am doing the Coursera course on DSP by Prandoni and Vetterli, and was excited to learn that we can use the tools of vector spaces to analyze discrete signals. At this early point in the course the ...
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Error bounds in signal compression represented by truncated Moore-Penrose biorthogonal bases using von Neumann wavelets

I was reading and trying to reproduce the results in the arXiv preprint of Periodic Gabor Functions with Biorthogonal Exchange: A Highly Accurate and Efficient Method for Signal Compression by Asaf ...
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Recovering eigenvalues from singular values [closed]

I am dealing with a problem similar to principal component analysis. Aka, I have a matrix and i want to recover the 'most efficient basis' to exaplin the matrix variability. With a square matrix these ...
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Ideas on matrix factorizations and/or transformations for $\ell_1$ minimization

I am starting with a typical $\ell_1$ basis pursuit problem: $$ \min_{\mathbf{x}} \Vert \mathbf{x} \Vert_1 \quad \mathrm{s.t.} \quad \Vert \mathbf{ERx} - \mathbf{y} \Vert_2 \leq \epsilon, $$ where ...
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191 views

why eigenvalues concerned in Harris corner detection?

In Harris corner detection, as I see, the goal is to find out those points $(x,y)$ which makes $S(x,y)$ a large value for any direction of shifting, $$ S(x,y) = [\Delta x , \Delta y]M\left[ ...
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How do you combine 2 least squares estimators? [duplicate]

Say you want to compute the least squares estimate of $w$ from a data-set: $$ \begin{bmatrix}d_1 \\d_2 \\\vdots\\d_N \end{bmatrix} =\begin{bmatrix} x_1 \\x_2 \\ \vdots \\x_N\end{bmatrix}w + ...
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Panorama global registration

I'm trying to do global registration algorithm for panorama like described here. But I don't understand how they deal with false pairs. Also if expand the system u1*I*P1=u1*I => P1=I ...
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127 views

How can a linear operator on DFT vector produce the same vector using only half of the DFT vector?

Suppose there is a DFT vector $\mathbf{X}$ with length N, which presents complex conjugate symmetry around its middle point, i.e., $X(1) = X(N-1)^*$, $X(2) = X(N - 2)^*$ and so forth. $X(0)$ and ...
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221 views

Conditions for precoding matrix to preserve complex conjugate symmetry on DFT vector

Suppose there is a DFT vector $\mathbf{X}$ with length N, which presents complex conjugate symmetry around its middle point, i.e., $X(1) = X(N-1)^*$, $X(2) = X(N - 2)^*$ and so forth. X(0) and X(N/2) ...
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898 views

How to compute generator matrix from a parity check matrix?

I have a parity matrix ("H") that is not in canonical form (the identity matrix is not on the right side). I'm trying to programatically calculate the generator matrix ("G") from it. The Wikipedia ...
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113 views

Doubt on Weighted Least Square Estimation

This is a page from the book linear algebra,geodesy and gps by Gilbert Strang.... the page explains about the justification of the inverse of the of the co variance matrix of measurement vector $b$ ...
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111 views

Least Square Error Estimation doubt when can we write $(A^TA)^{ -1} = A^{-1}(A^T)^{-1}$?

I am new to linear algebra and have this simple question... in least sqaure estimation...the best estimation of the equation $Ax = b$ is $x_{Estimated} = A (A^t A )^{-1} A^t b$...the projection of $b$ ...
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780 views

Good book or reference to learn Kalman Filter

I am totally new to the Kalman filter. I've had some basic courses on conditional probability and linear algebra. Can someone suggest a good book or any resource on the web which can help me can ...
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Mathematics of Harris corner point detection

This is the mathematical expression for Harris corner detection: But I have the following doubts: What is the physical significance of $u$ and $v$? Many references say it is the magnitude by ...
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Fitting new images from a SVD/PCA calculation

I'm trying to replicate the ideas from the Eigenface page on wikipedia. From a hundred sample images represented by a data matrix $\bf X$ (where each image flattened to a vector of length $n$, thus ...