1
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0answers
25 views

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 $q(k) \in \mathbb{R}^{Nn}$. ...
1
vote
1answer
52 views

Matrix exponential of a simple bidiagonal matrix

I am interested in finding an expression (closed form or recursive) for the matrix exponential of this banded matrix: $$ \begin{pmatrix} 0 & 1 & 0 & 0 & \cdots & 0 & 0 ...
0
votes
1answer
185 views

How to calc $\min ||J\Delta\tau + D||_*$

How to calculate $$ \min_{\tau} ||J_1 \tau_1 + \cdots + J_p \tau_p + D ||_* $$ where $\tau_1, \cdots, \tau_p \in \mathbb{R}$ $J_1, \cdots, J_p, D \in \mathbb{R}^{m \times n}$ $||\cdot||_*$ is sum ...
1
vote
1answer
44 views

Determinant of parametric function and $0!1!2!…n!$

As answer to this question, I trued to calculate the wronskian of: $$\left| \begin{array}{ccc} e^x & e^{2x} & ... & e^{nx}\\ e^x & 2e^{2x} & ...& ne^{nx} \\ e^x & 4e^{2x} ...
0
votes
0answers
80 views

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.
1
vote
1answer
35 views

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 ...
1
vote
1answer
131 views

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 ...
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votes
1answer
74 views

Get the closed-form using jordan normal form?

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 ...
1
vote
2answers
188 views

Looking for a closed form to determine whether a symbol is part of the ith combination nCr

Hi I'm new to this, feel free to correct or edit anything if I haven't done something properly. This is a programming problem I'm having and finding a closed form instead of looping would help a lot. ...