# Tagged Questions

42 views

13 views

### Consider a symmetric matrix $X$ with eigendecomposition $X=UVU^T$, how to call $\sum_{v_{k,k}>0}v_{k,k}u_ku_k^T$?

Consider a symmetric matrix $X$ with eigendecomposition $X=UVU^T$ How do people call $\sum_{v_{k,k}>0}v_{k,k}u_ku_k^T$? Sum of positive components of $X$? The positive semi definite part of $X$? ...
36 views

### Approximate Equivalent To Michael Spivak's text, “Calculus” but for Linear Algebra?

Does anyone know of an approximate equivalent To Michael Spivak's text, "Calculus" but for Linear Algebra? I love the way this book is written! It is simultaneously rigorous and thorough without ...
8 views

21 views

### Reference request for topic “Change of coordinate matrix”

I recently started with vector spaces. I understood every theorem from the course book uptil isomorphism. Then, i saw this particular topic and was totally blank. I don't know whether it was the ...
15 views

### How to test if $m$ vectors are linearly dependent when they are $n$ dimensional and $m < n$

I'll be shocked if this isn't a duplicate, but I haven't had a lot of luck finding an answer to this so far. How do you test if a set of vectors $v_1, \ldots v_m \in \mathbb{R}^n$ are linearly ...
70 views

### How to understsand eigenvalues and eigenvectors.

I know basic linear algebra (what is a matrix, what is a determinant, what is a square matrix, what is an inverse of a matrix, how to add/sub/multiple matrices etc.) But I am finding the concept of ...
62 views

### Inner Product Spaces, suggestion for book.

Can you suggest me name of some books which would help me visualize IPS better? Like, books having diagrams and stuff?
20 views

### Largest average principal submatrix of a symmetric matrix.

I am wondering if there exists literature on the following problem: Let $X$ be an $n \times n$ symmetric matrix. How do you identify the $k \times k$ principal submatrix of $X$ with the largest ...
506 views

### Very good linear algebra book.

I plan to self-study linear algebra this summer. I am sorta already familiar with vectors, vector spaces and subspaces and I am really interested in everything about matrices (diagonalization, ...), ...
43 views

### Existence and construction of asymmetric codes

By a $[n,k]_2$-code I mean a $k$-dimensional $\mathbb{F}_2$-subspace of $\mathbb{F}_2^n$. Such a code $C$ admits a symmetry $\sigma \in S_n$ if for any word $w \in C$ we also have $w^\sigma \in C$, ...
23 views

### Linear Optimization Study Material

I've recently enrolled in a linear optimization course, and it's been a while since I've taken linear algebra. I do not yet have access to the book for the course or I would skim it to see what I need ...
34 views

### Regular matrices references

Can someone suggest me a book or a lecture note which covers regular matrices with all theories related to it? Any assistance will be much appreciated. (By regular I mean some power of the matrix is ...
124 views

### Choosing good textbooks in linear algebra, analysis and graph theory

I need some advices to choose good undergraduate textbooks in LINEAR ALGEBRA, ANALYSIS and GRAPH THEORY. I found: Gilbert Strang // Introduction to Linear Algebra - Welleslay Cambridge Press (2009) ...
13 views

### Reference request: Tensor Product of $m$ $SU(N)$ algebras

I'm working on quantum mechanics of linear $SU(N)$ chain of sites. Specifically, I would like to study a Tensor product of $m$ Lie algebras $\mathfrak{s}\mathfrak{u}(N)$  V\in SU(N)\\ W = ...
43 views

### Is every element of a complex semisimple Lie algebra a commutator?

Let $L$ be a (finite-dimensional) complex semisimple Lie algebra. Then we know that $L = [L,L]$. Is it true that every element of $L$ must be a commutator? Since a complex semisimple Lie algebra is ...
61 views

### categorification and linear algebra

Vect is the category with objects as vectors and arrows as linear transformations between them. Then these arrows have quite a bit of structure. We can take the transpose, trace, determinant, ...
27 views

### Sylvester domains

I'm an undergrad mathematics student and I'd like to request some books about Sylvester domains. Specifically I'd like to understand the fact that not all modules are Sylvester domains. I just proved ...
366 views

### Book recommendation for Linear algebra.

I am looking for suggestions, it has to be a self study book and should be able to relate to applications to real world problems. If it is more computer science oriented , that would be great.
56 views

### Matrix representation of complex numbers in exponential form

Do there exist matrices M and P for this equation? Or perhaps M and P dont need to be matrices? I saw this and this question after googling which made me wonder about whether the exponential form of ...
47 views

### Arbitrary (i.e. not necessarily finite-dimensional) vector spaces; reference request.

Its virtually impossible to complete an undergraduate degree these days without studying finite-dimensional vector spaces in quite some detail. So like most of us, I've done all that; however, just ...
16 views

### Books in spectral theory for finite dimensional spaces

I'm looking for beginner books of spectral theory for finite dimensional spaces. I've already heard about this subject, but I don't know where I can find it. What's the domain of this subject? (Linear ...