# Tagged Questions

**23**

votes

**6**answers

1k views

### Does seeing beyond the course you teach matter? The case of linear algebra and matrices

This question is indeed very important for me. Thus I hope you bear with my subjective explanations for a few minutes. I am an "excellent" lecturer, at least according to course evaluation forms ...

**1**

vote

**0**answers

402 views

### Linear Algebra Text Book

In our department we do not like our current linear algebra book and so we would want to find a better book. This is for the first course in linear algebra and the title of the course is
Elementary ...

**2**

votes

**4**answers

397 views

### Eigenvalues of powers of linear mappings

Let $\tau$ be a linear map on a finite dimensional complex vector space. Clearly, if $\lambda$ is an eigenvalue of $\tau$ then $\lambda^n$ is an eigenvalue of $\tau^n$, for any natural (integer, on ...

**15**

votes

**3**answers

943 views

### Research level applications of “row rank = column rank”?

No less an authority than Gilbert Strang frames "row rank equals column rank" (and a couple of other facts) as "The Fundamental Theorem of Linear Algebra."
I'd simply like to assemble (for teaching ...

**22**

votes

**13**answers

2k views

### Elementary applications of linear algebra over finite fields

I'm teaching axiomatic linear algebra again this semester. Although the textbooks I'm using do everything over the real or complex numbers, for various reasons I prefer to work over an arbitrary ...

**1**

vote

**3**answers

379 views

### Continuous change of basis (and on the definition of determinant) [closed]

Let $(u_1, \ldots, u_n)$ and $(v_1, \ldots, v_n)$ be two ordered bases of $\mathbb R^n$. The orientation of the first basis is defined as the sign of the determinant of $[u_1 \cdots u_n]$, and ...

**4**

votes

**1**answer

612 views

### Is Diagonalization worth to be taught? [closed]

When students come to the College (first two years of the University system in most of the developped countries) to train in mathematics, they get a linear algebra / matrix analysis course. After a ...

**5**

votes

**5**answers

886 views

### Topics for a matrix analysis course

I recently taught a new (to my department) course titled "Matrix Analysis". For various reasons that I won't go into here, I was dissatisfied with the textbook I (loosely) followed, and with every ...

**7**

votes

**2**answers

2k views

### What is the dual concept to “annihilator” called, and do any linear algebra textbooks discuss this concept first?

When introducing dual spaces for the first time, most linear algebra textbooks proceed in what seems to me a rather backwards fashion: the annihilator $\{f\in V^*: f(u)=0\quad \forall u\in U\}$ of a ...

**10**

votes

**7**answers

1k views

### Proof that bases etc. exist in early linear algebra course?

I'm currently struggling to teach a 2nd course on linear algebra (in the UK, not at an Oxbridge quality university: the students have done a 1st course which concentrated upon algorithms you can apply ...

**28**

votes

**20**answers

6k views

### Why linear algebra is fun!(or ?)

Edit: the original poster is Menny, but the question is CW; the first-person pronoun refers to Menny, not to the most recent editor.
I'm doing an introductory talk on linear algebra with the ...

**16**

votes

**13**answers

4k views

### Pedagogical question about linear algebra

Last semester I taught a linear algebra class that is intended to introduce young students (at a sophmore-junior level) to "abstract mathematics". It seems that a major conceptual hurdle for many of ...