Tagged Questions

3answers
55 views

Index notation for inverse matrices

I have a question: There is an standard way to write the inverse of a matrix in index notation?. The reason is that I don't want to write $(A^{-1})_{ij}$ or $(A^{-1})_i^j$ or $(A^{-1})^{ij}$ using ...
1answer
78 views

Why we use $\mathbb{R}^{m \times n}$ notation instead of $\mathbb{R}^{n \times m}$?

I just realised, that I use all the time the notation $\mathbb{R}^{n \times m}$, and all books and papers use $\mathbb{R}^{m \times n}$. $\mathbb{R}^{n \times m}$ is more sympathetic for me, because I ...
1answer
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 $X$? ...
2answers
32 views

Scalar to the power vector

I have a formula that contains $\log (I + e^{X})$ term where $X$ is an $N$ dimensional vector ($x_0, x_1, ..., x_{N-1}$) and $I$ is the unity vector. I don't know how the exponentiation and log ...
2answers
29 views

Let $V$ be the set of all ordered pairs of real numbers, and consider the following addition and scalar multiplication operations on $u$ and $v$

I'm confused on b) and c) , what do the terms in it mean? I'm also having trouble finding e) ..
3answers
805 views

Meaning of math symbol ~

Segment of Example: t = ... More usefully, we have: t ~ n*log(n) Note: ~ means "similarity" like in geometry, same shape but not same size. How is it interpreted here? Edit: yes, t depends on n ...
2answers
72 views

Dot product notation

Let $\mathbf{A=(a_1,a_2,\ldots, a_n)}$ and $\mathbf{B=(b_1,b_2,\ldots,b_n)}$. Many linear algebra books and texts define the dot product as $$\mathbf{A\cdot B^T=a_1b_1+a_2b_2+\cdots+a_nb_n}$$ where ...
2answers
55 views

Both Linearly Independent and Dependent?

Is it possible for two vector functions of, for the moment's simplicity, one variable be both independent and dependent? The reason I'm asking this is because on a problem from a book of mine (not ...
0answers
22 views

element subset for adjacency matrix

I am trying to create an element of a matrix that is a subset of a larger matrix. However, I am told that my subscripts do not match. I wanted other people's opinion as to what I am doing wrong and ...
2answers
57 views