1
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1answer
54 views

Can I use the pseudoinverse of a Jacobian like I think I can?

I need to compute the Jacobian for a transformation that maps parameters $p_1,...,p_n \to q_1,...,q_m$, $n\neq m$. For this, I need to compute the derivatives $\frac{\partial p_i}{\partial q_j}$. ...
1
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1answer
67 views

Distribution of the Inverse of a Random Variable

I am trying to figure out how to find the distribution of the inverse of a random variable. Say, $Y=X^{-1}$ where X can take negative values. The two ways I know to find the distribution of a random ...
0
votes
1answer
53 views

Transpose of 2 matrices together

So if I have an $m\times n$ matrix $A$ and I represent that matrix as $\displaystyle A = QR$, how do I write $A^{T}$ (transpose) in terms of the original $\displaystyle QR$? Does it become ...
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2answers
2k views

RYB and RGB color space conversion

I am working on a project where I need to convert colors defined in RGB (Red, Green, Blue) color space to RYB (Red Yellow Blue). I managed to solve converting a color from RYB to RGB space based on ...
1
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3answers
492 views

Is this an invertible linear transformation?

Suppose you have a linear transformation $T: M_{2\times 2}\to M_{2\times 2}$ given by $$ \begin{pmatrix} a & b \\ c & d\end{pmatrix}\mapsto \begin{pmatrix} a+b & a \\ c & ...
2
votes
1answer
201 views

Linear Algebra Question ( rank of matrix )

Let $\bf A$ be an $m \times n$ matrix. If $\bf P$ and $\bf Q$ are invertible $m \times m$ and $n \times n$ matrices, respectively prove $\operatorname{rank}(\mathbf{PA}) = ...