# Tagged Questions

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### Properties determining boundedness of function

The function I am looking at is $$f(x) = \frac{1}{2}x^TAx + b^Tx + c$$ where $A$ is a symmetric matrix in $\mathbb{R}^{n\times n}$ and $b,c$ belong to $\mathbb{R}^n$ I want to determine what ...
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### Minimize the Frobenius norm of the difference of two matrices with respect to matrix: $\underset{B} {\mathrm{argmin}} \left\| A- B \right\|_F$

The following question is similar to this one, but I think that it is not straightforward to move from one to the other, so please take a look. Otherwise, please let me know and I will delete it. ...
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### the differences and relationship between linear independent and affinely independent

When learning optimization, I heard the two related concepts on linear algebra: linearly independent and affinely independent. ...
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### Convex matrix inequality

Consider a matrix inequality as $M(a,b,c)<0$ where $a>0$, $\bar b>b>0$ and $c\in[-1, 1]$. The problem is feasibility of this inequality for all the possible values of the parameters. Can I ...
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### total least squares derivation with matrices

Taken from a computer vision book: "to minimize the sum of the perpendicular distances between points and lines, we need to minimize $$\sum_i (ax_i + by_i +c)^2$$ subject to $a^2 +b^2 =1$. Now using ...
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### Gradient of matrix exponential function

Grateful if somebody could help me with the following. I am trying to find the gradient of the next expression: $$f(a_1, a_2, a_3, a_4)=\Vert R*y-x \Vert$$ where $y$ and $x$ are known 4x1 column ...
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### Minimizing Frobenius norm for two variables

I need to minimize squared Frobenius norm: $\|\mathbf{A} - \mathbf{x}\mathbf{y}^T\|_F^2$. Namely I need to prove that for this norm to reach minimum $\mathbf{x}$ should be eigenvector of ...
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### How to find center and radius of hand-drawn circle? [duplicate]

You are given a set of points {(X1,Y1), (X2,Y2),...} which represent a hand-drawn circle, so it's not perfect. You are asked to find the center and radius of this circle. My intuition tells me this ...
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### Matrix Optimal Strategy Problem

(B) What is the expected value of the game for R if the bank R always chooses TV and bank C uses its optimum strategy? E= _ (type fully reduced fraction or mixed number) (C) What is the expected ...
Let $\mathbf{A}$ be a $N\times N$ positive semi-definite hermitian matrix. Let $\mathbf{b}$ be a $N\times 1$ complex vector. For any given constant $t$, I interested in the minimum eigenvalue of the ...