Questions tagged [linear-algebra]
For questions related to linear mappings, matrices, basis, determinants, eigenvalues and other topics commonly done in a linear algebra course.
85
questions
11
votes
1
answer
1k
views
Is Lax's Linear Algebra and its Applications comprehensive or idiosyncratic?
I'm looking for a good abstract linear algebra text (i.e., not matrix crunching) for students who have completed a Strang-level linear algebra course plus exposure to a proof writing (e.g., induction ...
user9185
11
votes
1
answer
524
views
Helping a student exasperated by abstract concepts in linear algebra
I am currently tutoring a student in linear algebra. She is a very hard worker and does well on computational problems, but struggles to build mathematical intuition. This struggle is compounded by ...
- 1,247
3
votes
1
answer
99
views
Resources on 3D transforms, vectors, coordinate systems
Background: I'm helping engineers use software to create 3D geometry in a programmatic way (similar to OpenSCAD). The functions they need to call have inputs which are low-level geometry concepts: 3D ...
- 131
4
votes
2
answers
250
views
Determinant applications for 16 year olds
I am teaching matrices, determinants and systems to a class of 16-year-olds.
As you can expect, they do not know calculus or linear algebra.
What they do know is a little bit of matrices (how to ...
3
votes
3
answers
187
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 ...
- 241
10
votes
2
answers
328
views
How can one motivate the adjugate matrix?
The adjugate matrix of an $n \times n$ matrix $A$ is defined by $(\mathrm{adj}\ A)_{k\ell} = (-1)^{k+\ell}\,\det M(\ell,k)$, where $M(\ell,k)$ is the minor matrix obtained from $A$ by deleting row $\...
- 859
7
votes
3
answers
216
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'...
- 71
20
votes
4
answers
919
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 ...
- 655
16
votes
7
answers
1k
views
Why do we teach that every line is a linear function?
Teaching my precalculus class today, I noticed something very simple that I hadn't taken into account previously. The definition in our textbook read:
"A linear function is a function defined by ...
- 1,746
13
votes
2
answers
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 ...
- 17.1k
15
votes
6
answers
672
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 ...
quid♦
- 7,622
10
votes
5
answers
673
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 ...
- 2,571
25
votes
6
answers
886
views
Too much motivation?
This is something that I felt like was difficult for me in some classes, especially lower division differential equations and linear algebra classes. I know professors want to motivate certain topics ...
user5108
9
votes
3
answers
231
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 ...
- 191
14
votes
3
answers
447
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 ...
- 242
3
votes
2
answers
468
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 ...
- 549
18
votes
1
answer
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 ...
- 2,143
14
votes
4
answers
1k
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 ...
- 1,091
7
votes
1
answer
628
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 ...
- 699
8
votes
3
answers
5k
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 ...
- 1,091
8
votes
3
answers
3k
views
Self-study Linear Algebra textbook for Machine Learning and Statistics
I am looking for a good linear/matrix algebra textbook, suitable for self-study, that covers topics relevant to statistics and machine learning. I have access to ...
- 221
7
votes
1
answer
202
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 ...
- 171
15
votes
1
answer
2k
views
Proving theorems on one's own: how long should one persist?
I've recently started learning linear algebra on my own. I always try to prove the theorems I encounter by myself, without looking at the book (only to check if my proof is correct), because I found ...
- 253
10
votes
2
answers
585
views
Textbook for 2nd linear algebra course
I am teaching (for the first time) a 2nd course in linear algebra. The students will have had a beginning course in linear algebra and a beginning course in abstract algebra. I am considering Hoffman ...
- 139
3
votes
0
answers
49
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 ...
- 139
13
votes
14
answers
3k
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 ...
14
votes
2
answers
2k
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, ...
- 1,508
10
votes
2
answers
563
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 ...
- 815
11
votes
1
answer
262
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 ...
- 5,955
6
votes
3
answers
198
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 ...
- 9,122
7
votes
4
answers
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 ...
user230
15
votes
5
answers
954
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 ...
- 28.9k
20
votes
6
answers
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:
...
- 8,079
25
votes
13
answers
3k
views
What is a good motivation/showcase for a student for the study of eigenvalues?
Courses about linear algebra make great demands on looking for eigenvalues and transforming matrices to diagonal matrices (or, at least, to Jordan normal form). This is somehow a technical, recipe-...
- 9,122
14
votes
3
answers
624
views
Why teach back substitution with row reduction?
Many linear algebra books include two versions of row reduction for solving systems of linear equations:
(1) Reduce to echelon form, and then use back substitution.
(2) Reduce to reduced echelon ...
- 8,079