# Questions tagged [singularvalues]

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136 questions
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### If A is a nxn singular matrix, then it has a singular value = 0

This is a question on a testexam. But am I correct in assuming that a singular matrix has det = 0, which gives it an eigenvalue of 0 and that gives it a singular value of 0?
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### Do I get better solution if I have more data - Pseudo Inverse

I wonder if I can get a better solution for this equation: $$Ax = b$$ If $A$ is not square and I use pseudo inverse $A^{\dagger}$ to find $x$ $$x = A^{\dagger}b$$ The reason why I asking this is ...
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### Is it possible to compute the eigenvalues and eigenvectors if I know the svd?

I have a matrix $A$ ...
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### Given the $SVD$ of a matrix comprised of centered data points in $R$3, how do I find the line of best fit through the origin?

I'm slightly confused by this question - from my understanding the vectors u in $U$ are first principal components. In that case, would they already compose the line of best fit through the origin (...
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### Relationships between top-$k$ eigenvector and top-$k$ singular vector of symmetric matrix $A$

Is there any relationships of top-$k$ eigenvector and singular vector of symmetric matrix $A \in R^{n \times n}$? For symmetric matrix $A$ its eigenvalue decomposition is: $$A = B \Lambda B^T$$ ...
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### U matrix in Singular value decompositon.

I know that the Singular Value Decomposition of a matrix $X$ is given by: $X = U\Sigma V^T$, where $U$ and $V$ matrices are column orthonormal and $\Sigma$ is a diagonal square matrix containing ...
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### If $A= (QU_2)\begin{bmatrix}\Omega_k & O\\ O& \Lambda\end{bmatrix} (PV_2)^T$, When will diagonal elements of $\Omega_K, \Lambda$ be singular values?

Suppose we show $$A= (QU_2)\begin{bmatrix}\Omega_k & O\\ O& \Lambda\end{bmatrix} (PV_2)^T$$ where $\Omega_k$ and $\Lambda$ are the diagonal matrices from the SVD of two other matrices. When ...
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### nocedal and wright singular values bounded away from zero

In the Nocedal and Wright Numerical optimization second edition book, pages 255-256, they state that the Jacobians "$J(x)$ have their singular values uniformly bounded away from zero in the region of ...
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### To prove that $\vec{u_3}$ is a left singular vector of $A$

Question: Let $A$ be a $3*2$ matrix with $rank(A)=2$. Let $\sigma_1$ and $\sigma_2$ denote the singular values of $A$. Let {$\vec{v_1},\vec{v_2}$} be an orthonormal basis for $R^2$ of right singular ...
### Finding the maximum value of $A\vec{x}$ when $||\vec{x}||= 1$
Question: If $A= \begin{bmatrix} 1&0&1\\1&1&-1 \end{bmatrix}$ and $\vec{x}$ is an element of $R^3$. It is given that $||\vec{x}|| =1$. I have to find the maximum value for $A\vec{x}$. ...