# Tagged Questions

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### Closed-form expression for this matrix equation?

I have the following matrices $P \in \mathbb{R}^{N \times N}$, $q(k) = \begin{bmatrix} q_1(k) \\ \vdots \\ q_N(k) \end{bmatrix}$. With $q_i(k) \in \mathbb{R}^n$ and thus $q(k) \in \mathbb{R}^{Nn}$. ...
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### Closed form for matrix multiplication

Let Q be a n by n positive definite or positive semi definite matrix and g be a vector in $R^{n}$. Is there a closed form to get x? $g^{T}Q^{k}g = x(g^{T}Qg)$ where k is a some integer number.
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### Minimization of $\text{tr} (W^TMW)-\text{tr}(NW)$ subject to $W^TW=I$

Is there a closed-form solution for finding W that minimizes the objective function: $\text{tr} (W^TMW)-\text{tr}(NW)$ subject to $W^TW=I$ where $M$ and $N$ are fixed matrices. I find it difficult to ...
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### Functions to pick up orderly the elements on the SW-NE half diagonals in a half matrix (lower triangular part)

I wish to write a program that does the following, and I need some math help figuring out a simple formula to pick up elements in the lower triangular part of a matrix. Consider the lower bottom-left ...
I have got the following transition matrix: $$A = \begin{pmatrix} p & 1-p \\ 1-q & q \end{pmatrix}$$ How can one use the jordan normal form to get a closed-form to calculate such a values ...