# Tagged Questions

**48**

votes

**8**answers

8k views

### Should the formula for the inverse of a 2x2 matrix be obvious?

As every MO user knows, and can easily prove, the inverse of the matrix $\begin{pmatrix} a & b \\\ c & d \end{pmatrix}$ is $\frac{1}{ad - bc} \begin{pmatrix} d & -b \\\ -c & a ...

**6**

votes

**4**answers

784 views

### How to solve Ax=b incrementally ?

Hi, everyone.
What I am struggling is the following problem. I have a linear matrix equation $Ax=b$, where $A$ is a known $n \times n$ large sparse real matrix, $x$ and $b$ are known $n \times 1$ ...

**0**

votes

**3**answers

995 views

### Intuitions/connections/examples for “eigen-*”

There are many concepts in mathematics that begin with the German word "eigen": eigenvector, eigenvalue, eigenspace, eigenstate, eigenfunction, eigensystem etc. (to name just the most important (?) ...

**6**

votes

**1**answer

1k views

### Is there good intution of the trace map?

I have never understood the trace map,not even after reading Geometric Interpretation of Trace. The problem with many answers in the above discussion is the geometric intuition does not apply to other ...

**15**

votes

**3**answers

840 views

### elementary Ext^1 intuition

I am wondering what sort of basic basic intuitive meaning Ext1(M,N) has.
As a base case: if ...