Tagged Questions
3
votes
2answers
47 views
Matrix Multiplication Definition
I'm sure everyone already thought about this at least one time.
Why matrix multiplication is not defined the way showed below?
$$\left( \begin{array}{ccc}
a_{11} & a_{12} & \ldots \\
a_{21} ...
4
votes
1answer
58 views
Importance of eigenvalues
I know how to find eigenvalues and eigenvector .But I dont know what to do with that.
What is there use? Can anyone explain me that?
2
votes
4answers
153 views
How does linear algebra help with computer science
I'm a Computer Science student. I've just completed a linear algebra course. I got 75 points out of 100 points on the final exam. I know linear algebra well. As a programmer, I'm having a difficult ...
1
vote
0answers
51 views
Properties of Non-Diagonally Dominant Matrix
I have a question about properties of matrices which are or are not diagonally dominant.
So I understand that a diagonally dominant Hermitian matrix with non negative diagonal entries is positive ...
11
votes
3answers
121 views
Are matrices best understood as linear maps?
Any linear map between finite-dimensional vector spaces may be represented by a matrix, and conversely. Matrix-matrix multiplication corresponds to map composition, and matrix-vector multiplication ...
4
votes
2answers
62 views
Books for linear algebra over commutative rings
I was thinking about reviewing linear algebra to recover many theorems that I can use over commutative rings with unity. But it seems very tedious and I did not want to make any mistakes on these ...
3
votes
1answer
54 views
Motivation for the double dual
I was reading on the double dual of a vector space $V$ recently. I was wondering what applications (within mathematics) there are for this concept and/or what was the motivation for the development of ...
3
votes
1answer
66 views
Presentation, Reduction and Generalization in Mathematics: The Case of Linear Algebra
Apologies for the grandiose title, but it is motivated by a serious consideration. Linear algebra, LA hereafter, is an enormously interesting area of mathematics. What's more, it is fairly ...
1
vote
0answers
58 views
DFT shift theorem generalizations?
The DFT shift theorem implies that any circular shift in the input space is equivalent to a phase change in the frequency domain, while the absolute values are preserved.
$$
...
1
vote
2answers
123 views
What is a intuitive proof of multivariable changing of variables formula (jacobian) without using mapping and/or measure theory?
What is a intuitive proof of multivariable changing of variables formula (jacobian) without using mapping and/or measure theory?
I was thinking that textbooks make the proofs over complicate.
If ...
35
votes
11answers
2k views
Why study linear algebra?
Simply as the title says. I've done some research, but still haven't arrived at an answer I am satisfied with. I know the answer varies in different fields, but in general, why would someone study ...
0
votes
1answer
65 views
What is meant by “orbit” in this question?
I was reading "Prove that Anosov Automorphisms are chaotic," and the answer and a few of the comments talked about orbits. I'm curious what is meant by "orbits" in the given context. Is it analogous ...
2
votes
3answers
276 views
Soft question: Why freshmen feel linear algebra is abstract?
When I was a freshman, I have learnt linear algebra for two semester. I feel linear algebra is abstract and hard to truly understood. For example, my textbook introduce the concept "nonsigular" by ...
1
vote
1answer
60 views
can somebody tell me the name of the next theorem?
I am looking for the name of the next simple fact(theorem):
let $M$ be some matrix and let $k$ be some combinatorial rectangle in $M$. denote the matrix of $k$ by $M_k$.
It holds that:
$Rank(M)\ge ...
2
votes
4answers
162 views
Understanding matrices as linear transformations
I am currently taking a intro course to abstract algebra and am revisiting ideas from linear algebra so that I can better understand examples.
When i was in undergraduate learning L.A. i thought of ...
