# 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 ...

56 views

32 views

### Clarification on Homomorphism and Automorphism of Vector Spaces

I've been struggling to connect some of these concepts for a while now and seem to be confusing myself more than helping myself by continuing to think about them. Could someone confirm or deny my ...
135 views

### Orthonormal and/or Orthogonal Basis of a Pair of Vectors

I was hoping someone could verify if this is the correct way to answer this problem: Let $\mathbb{R^{2}}$ have the standard dot product. Classify the following pair of vectors as (i) basis, (ii) ...
39 views

### Prove that T1+T2 and cT1 are linear transformations

Sorry to ask two questions in a day, but I was struggling with this problem. I'm probably overthinking it. If $T_1$ and $T_2$ are linear transformations from V into W, verify that $T_1+T_2$ and ...
47 views

### What are the objects and morphisms of the category $\operatorname{Vect}$?

What are the objects and morphisms of the category $\operatorname{Vect}$? I am trying to learn category theory, and it seems we have infinite objects in $\operatorname{Vect}$ being all of the finite ...
38 views

### Matrix computing of $a(i,j)a(j,i)$

I have a square, semi-positive matrix $A$ and I want to compute the sum of the products $a(i,j)a(j,i)$ for every $i$ and $j$. Is there any easy way to perform this computation that does not involve ...
94 views

38 views

### How to find a partial derivative with respect to a matrix?

Let we have a $2\times2$ matrix $A=\begin{bmatrix}a_1&a_2\\a_3&a_4\end{bmatrix}$, a $1\times2$ matrix $C$, and a $2\times1$ matrix $X$. How can we calculate derivative of $CAX$ with respect to ...
Let $A$ be an $n\times n$ matrix. Let $q_A(t)$ and $p_A(t)$ represent the minimal and characteristic polynomial respectively. Then, the following are equivalent: (a) ...