# Tagged Questions

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### Transform gradient to reference element

Minimal example of the problem My attempt I think this is not a linear solution like $$\nabla u = \nabla A_K x + \nabla b_K$$ which must be wrong because $A_K$ is a ...
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### Given $A$, find invertible $B$ such that $B^{-1}AB$ is positive

Given $A \in Mat(n,n,\mathbb R)$, is there always an invertible matrix B, such that $B^{-1}AB$ is positive, assuming all eigenvalues of A are positive and simple ? If yes, is it possible to classify ...
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### Getting linear combinations in linear algebra?

I failed a homework problem a few days ago. I can't figure out how they got the answers, which have been given in green as corrections. Help me figure how they got them;
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### Constructing regular integer matrices with distinct integer eigenvalues

How can I construct matrices with positive integer values and distinct integer eigenvalues (not necessarily positive, but 0 should not be an eigenvalue). The standard-method to construct matrices ...
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### Show $rk(A) + rk(B) \ge rk(A+B)$

Show $rk(A) + rk(B) \ge rk(A+B)$, where $A,B \in M_{m\times n}(\mathbb{F})$ I'm trying to think in terms of linear transformations. We can define $T_a, T_b:\mathbb{R}^n\rightarrow \mathbb{R}^m$ I ...
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### $3D$ projection onto a plane

I have an engineering problem involving math so I figured I ask it here. I have two sets of data: Acceleration in $3$ dimension is given by $\langle X,Y,Z \rangle$. Change of orientation along ...
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### Composite linear map Rank and Image

I have been pondering on this question, I did part $(a)$ wherein you had to prove that $\operatorname{Im}(T)= \operatorname{Im}(T^{2})$ , but I am struggling to get the concept of part $(b)$, any help ...
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### How can I combine affine transformations into one matrix?

So from what I understand from this picture, the box is stretched to twice its width. And it is then flipped from the x-axis. And then it is rotated 30 degrees anticlockwise. So these three ...
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### Find angle-preserving transformation matrix given 2 points

I asked a similar question yesterday about finding an affine transform matrix given the same 2 points in both coordinate systems. I was told that there was only a unique solution, if the scaling was ...
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### Find 2D affine transform matrix given a pair of points

I have the coordinates of two points in an initial 2d coordinate system and the corresponding coordinates in a target system. Is is possible to determine the affine transform matrix from these values? ...
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### Function that transforms a Matrix to different dimensions

What is the name of a function that transforms a matrix into different dimensions? Say I have a matrix M of dimensions $(x,y)$ and I want to transform it to dimensions $(w,v)$. I can accomplish this ...
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### Constructing a similarity matrix between points

I have two images with two sets of corresponding points. In order to align the images I'm trying to compute the similarity matrix that describes the relationship between the corresponding points. I ...