Tagged Questions

Linear algebra is concerned with vector spaces of all dimensions and linear transformations between them, including systems of linear equations, bases, dimensions, subspaces, matrices, determinants, traces, eigenvalues and eigenvectors, diagonalization, Jordan forms, etc. For questions specifically ...

23 views

The Matrix of a reflection (around abitrary plane)

Let $\Upsilon :\mathbb{R}^3\rightarrow \mathbb{R}^3$ be a reflection across the plane: $\pi : -x + y + 2z = 0$. Find the matrix of this linear transformation using the standard basis vectors and the ...
12 views

Solving Systems of linear equations between a square matrix and a rectangular matrix with block decomposition

I am trying to decompose solving a system of linear equations using block decomposition where I have an (n x n) matrix A, which is a lower/upper triangular matrix, and a matrix B, which is a ...
24 views

Generate function from data

I have a series of inputs and outputs : Inputs -> Outputs 1,2,3 -> 4 4,5,6 -> 5 7,8,9 -> 6 Is there a field of study that can generate a single ...
6 views

How to linearize two discrete maps with time delay feedback

I have a 2-D system of two discrete maps $x_{n+1} = f(x_n) + P_1(y_n - y_{n-1})$, $y_{n+1} = g(y_n) + P_2(x_n - x_{n-1})$ with $g,f$ being smooth functions and $P_1, P_2$ belonging to the reals ...
23 views

prove that $A^{-1} = (1/detA) \operatorname{cof} A^T$

Can you please explain to me how to prove this theorem? Theorem: if $\det(A)\ne 0$, then $A$ is invertible and $A^{-1} = \frac 1{\det(A)} \operatorname{adj} A$
23 views

Change eigenvalues of correlation matrix and transform into original basis

I use the Random Matrix Theory to filter out the information from the correlation matrix that is associated with noise - Marcenko Pastur band. That is straight forward. Then I follow Rosenow, Bernd, ...
36 views

How to project $x_2$ onto $u_1$

I'm following a solution from here (the first problem), I don't understand how to "project $x_2$ onto $u_1$" 1) how does:$\begin{bmatrix}0\\\frac{1}{\sqrt{2}}\\\frac{1}{\sqrt{2}}\end{bmatrix}$ ...
8 views

16 views

15 views

Water drop evaporation time and contact angle

I'm measuring water drop evaporation on different surfaces and it would be nice to have an equation to roughly estimate evaporation time (or contact angle). Some drops are hydrophobic, others ...
35 views

What is a linear isomorphism?

I am working with the book Manifolds and Differential Geometry from Lee and I am a little bit puzzled since he sometimes talks about linear isomorphism (proposition 2.3 for example). But isn't an ...
55 views

39 views

what is Expected Mean

Thus the expected mean $\mu$ of the set $\mathcal S$ can be given as \begin{align*} \mathbb E \mu&= \sigma^2+\frac 1r \sum_{i=1}^m\left(\mathbb E\lambda_i-\sigma^2\right)\\ &\geq \sigma^2+\...
32 views