Questions tagged [linear-algebra]

For questions related to linear mappings, matrices, basis, determinants, eigenvalues and other topics commonly done in a linear algebra course.

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3
votes
3answers
181 views

Defining/introducing vectors informally

A vector is a collection of elements whose order matters. If the elements represent comparable measurements it can be said that they together represent a direction and a magnitude (length). The ...
7
votes
3answers
191 views

Solving linear systems - Applications

I was thinking today applications of $\textbf{Ax}=\textbf{b}$ where $\textbf{A}\in\mathbb{R}^{m \times n}$. Specifically, I am interested to know what applications one might give to students, who don'...
10
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2answers
483 views

Linear algebra for engineers

When studying linear algebra in mathematics (I mean, for the people studying mathematics) there are many ways of approaching it, depending of your needs, however supposedly every mathematician should ...
19
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4answers
880 views

Applications and motivation of abstract linear algebra topics for engineers

This semester I'm teaching introductory linear algebra for engineering students, and I don't think I'm doing a good job explaining why these topics are important; specifically, everything having to do ...
3
votes
2answers
404 views

Seeking your advice on books for abstract algebra and linear algebra

I am a college sophomore in the US with a major in mathematics and am an aspiring mathematician in the fields of computational complexity theory and cryptography. I would like to seek your advice and ...
13
votes
2answers
3k views

A simple explanation or derivation of Cramer's rule, suitable for secondary Algebra 2?

I am tutoring a high school student in Algebra 2. Her class has just covered systems of linear equations, mainly via the "substitution" and "elimination" methods. Her textbook concludes that unit ...
16
votes
6answers
612 views

How to get students in a under-graduate linear algebra course interested in determinants?

Before teaching the chapter on determinants in a linear-algebra course for beginning undergraduate students (mathematics and computer science, more specifically) I would like to give a small ...
10
votes
5answers
596 views

Textbook for first course in linear algebra

Since this does not appear to have been asked here before, I would like to solicit suggestions and recommendations, ideally with rationales, for a textbook in a first course in linear algebra. In my ...
10
votes
11answers
2k views

What is the best way to intuitively explain what eigenvectors and eigenvalues are, AND their importance?

How can we break down the complexity of eigenvalues/vectors to something that is more intuitive for students. I feel like the proofy way isn't a good intuitive representation of the mechanism that ...
9
votes
3answers
223 views

Teaching and motivating the use of Eigenvectors

I would like to know how to better demonstrate Eigenvectors. The texts that I have display the properties and methods to calculate them. There are plenty of great elementary examples to follow through ...
13
votes
3answers
420 views

Worksheet: Homology in Intro Lin Al

I am about to start grad school and I am trying to think seriously about teaching [you know, before I get swamped with my own coursework]. I wrote a hypothetical worksheet for an introductory linear ...
7
votes
1answer
187 views

What are the good sources for Singapore Mathematics?

I am looking for the conceptual/visualisation way of tackling the algebra problems . I found that Singapore Maths caters this need. What are the good sources for Singapore Maths - any online classes ...
14
votes
4answers
759 views

Key theorems in undergraduate linear algebra

I've been asked by an high school student what are the $5$ major theorems in Lang's Linear Algebra (and therefore, by extension, in an undergraduate linear algebra course). Firstly, I bluntly said ...
17
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1answer
1k views

Linear algebra textbooks presenting an eclectic, geometric approach to the subject

I am teaching an undergraduate course in linear algebra this fall. I am dissatisfied with most existing textbooks, and indeed with the way in which this subject is usually taught. I hope to find a ...
7
votes
1answer
593 views

How should I teach linear algebra and vector geometry together at high school?

I'm teaching mathematics at my former high school and the next topic will be vector geometry. When I attended high school, I was only taught vector geometry and never learnt anything about matrices ...
7
votes
3answers
4k views

Lang's Linear algebra or Introduction to linear algebra for an undergraduate

From a pedagogical as well as strictly mathematical perspective, which one of Lang's Linear algebra and Introduction to linear algebra would you recommend to an undergraduate with not much experience ...
3
votes
0answers
47 views

Text book for 2nd Linear Algebra course [duplicate]

I stumbled across this site while searching for Hoffman and Kunze. There was a discussion about using HK for a beginning linear algebra course. I am teaching (for the first time) a 2nd course in ...
20
votes
6answers
2k views

Is there a good way to explain determinants in an elementary linear algebra class?

Many colleges offer an an elementary linear algebra class for sophomore math, science, and economics majors. Such a class typically covers a chapter on determinants, including the following aspects: ...
14
votes
2answers
1k views

When is a good time to teach linear algebra?

When I was a student (in the 1970s) I was taught linear algebra as an "adjunct" to "engineering mathematics" such as differential equations. That was during my sophomore year, which seems a bit late, ...
15
votes
5answers
850 views

Should the cross-product in $\mathbb{R}^3$ be discussed in Linear Algebra?

I have not yet taught Linear Algebra, but I teach Computer Graphics regularly, which uses linear algebra at many junctures, and uses concepts such as the cross product. I have often been disappointed ...
11
votes
1answer
247 views

A more natural motivation for the appearance of generalized eigenvectors in linear system with repeated eigenvalue

When I teach constant coefficient linear differential equations, the usual guess of an exponential can be motivated because it is "approximately" a fixed point for the differentiation operator. The ...
6
votes
3answers
189 views

Should one visualize properties of a matrix or/and state its properties?

Sometimes, if you want students to manipulate some sort of special matrices (like, asking if they are invertible or ask for a LU decomposition, etc.), you have to possibility to state all properties ...
7
votes
4answers
3k views

Physics in Linear Algebra

Talking about physical phenomena related to a particular field of mathematics can be interesting for students and might further motivate their study of the subject. For instance, there are ...

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