1
vote
0answers
33 views

Matrices of the form $A^p=(a_{ij}^p)$

I am wondering if there is a name for these kind of matrices and if they are interesting or not? Do they even exist? Let $A$ be a $n\times n$ matrix with elements $a_{ij}$. $A= (a_{ij})_{i,j\in\{1, ...
3
votes
1answer
141 views

Hard problems book in linear algebra

Could you suggest me a book where I can find hard problems in Linear Algebra for an undergraduate student? Thanks in advance.
0
votes
1answer
135 views

Most “beautiful” presentations of the basic proofs for vector spaces?

I am familiar with the standard proofs presented in textbooks for stuff like linear independence/dependence, the dimensions of common vector spaces, any basis for a vector space V must be linearly ...
5
votes
3answers
250 views

Differences between infinite-dimensional and finite-dimensional vector spaces

I've just started a course in Representation Theory, and in solving our first homework I've used a couple of theorems about finite-dimensional vector spaces (for an example, rank-nullity theorem). My ...
5
votes
2answers
333 views

Abstract Algebra/ Linear Algebra classic problems [closed]

I am studying for an Algebra/Linear Algebra exam coming up in August.In preparation for my exam I have worked on a lot of problems from Dummit and Foote and Hoffman and Kunze' books. I would like to ...
7
votes
6answers
870 views

Finite vs infinite dimensional vector spaces

What familiar and intuitive properties of finite dimensional vector spaces fails in infinite dimensions? For example: In infinite dimensions there are non-continuous linear maps. In infinite ...
1
vote
0answers
65 views

Intuition on matrix multiplication and algorithms

Yesterday, I was watching Strang's lectures on Matrix multiplication. He mentioned five different ways of looking at the multiplication $\mathbf{AB} = \mathbf{C}.$ Classic way (Row of $\mathbf{A} ...
2
votes
1answer
55 views

Problems where SPD linear system arises

I know some of the places where SPD linar systems arises such as elliptic PDEs and normal equations. Can I have a more comprehensive list of scientific applications which require solving SPD linear ...
5
votes
4answers
5k 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
1answer
752 views

what is the most traditional abstract algebra textbook? and [Linear algebra & Abstract algebra] [closed]

I have listed 3 textbooks i have in my mind to buy Herstein - Topics in Algebra Artin - Algebra Lang - Undergraduate Algebra Unlike Lang's Algebra is the most traditional abstract algebra text for ...
2
votes
0answers
139 views

Properties about Matrices that can be proved by only using Block Multiplication of Matrices

I recently proved the property that product of two upper triangular matrices is an upper triangular matrices by using the block multiplication of matrices. The basic fact that was required to prove ...
10
votes
3answers
261 views

Deducing results in linear algebra from results in commutative algebra

Here are two examples of results which can be deduced from commutative algebra: Any $n\times n$ complex matrix is conjugate to a Jordan canonical matrix (can be proven using the structure theorem ...
7
votes
4answers
594 views

Cool/Useful Examples of Characteristic and Minimal Polynomials?

I'm teaching a Linear Algebra II undergrad course and for the section on characteristic & minimal polynomials, I really don't want to just give the students a bunch of matrices that have no ...
2
votes
2answers
2k views

Best books on A Second Course in Linear Algebra [duplicate]

Possible Duplicate: Prerequisites/Books for Linear Algebra I've studied from David Poole's Linear Algebra: A Modern Introduction However, it's not very complete. I want to study subjects as ...
9
votes
6answers
3k views

Prerequisites/Books for A First Course in Linear Algebra

What mathematical knowledge do I need to begin studying linear algebra? In particular, how much calculus do I need to know? Also, do you have a favorite linear algebra book you can recommend?
10
votes
7answers
7k views

practical uses of matrix multiplication

The use of matrix multiplication is usually given with graphics initially (scalings, translations, rotations, etc). Then there are more in-depth examples such as counting the number of walks between ...
11
votes
6answers
1k views

Non-numerical vector space examples

I've recently been thinking about why my peers and other people I've helped learn vector spaces had trouble intuitively understanding the concept, and it occurred to me that non-numerical (i.e. ...
23
votes
11answers
3k views

Fun Linear Algebra Problems

I'm teaching a linear algebra course this term (using Lay's book) and would like some fun "challenge problems" to give the students. The problems that I am looking for should be be easy to state and ...
6
votes
3answers
338 views

Are there variations on least-squares approximations?

In least-squares approximations the normal equations act to project a vector existing in N-dimensional space onto a lower dimensional space, where our problem actually lies, thus providing the "best" ...
14
votes
6answers
4k views

Real world uses of Quaternions?

I've recently started reading about Quaternions, and I keep reading that for example they're used in computer graphics and mechanics calculations to calculate movement and rotation, but without real ...