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Questions about Mathematica functionality related to manipulating vector spaces and linear mappings between such spaces. This includes determination of matrix properties, matrix transformations, decompositions, and factoring.

2 votes
Accepted

Solving an eigenvalue problem

Three modifications: add dependence on $x$ and $y$ (add [x_,y_] to the definitions and [x,y] to where the script letters are referenced), remove the & (this defines ℒ as an unnamed function which shou …
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1 vote

Coordinate transformation can this be done with AffineTransform?

To clear up ambiguities, the following code finds the transformation from the points in xy space $(0,1),(1,0)$ and $(0,0)$ to the points in uv space $a,b$ and $c$ projected onto $\overline{ab}$ respec …
Adam's user avatar
  • 4,006
2 votes

How to find the angle of a rotation matrix

For the matrix $\begin{bmatrix}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{bmatrix}$, your code computes $\frac{180}\pi\arccos(-\frac12+\cos\theta)$, so strange answers are expected (for instanc …
Adam's user avatar
  • 4,006