# Tagged Questions

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### Matrix-Multiplication

I have to matrices: $$A=\pmatrix{1&a&1\\1&0&a\\1&2&0} ; \quad B= \pmatrix{1&b&3\\2&1&0}$$ The task is to determine $AB, AB^T, BA$ I think i cannot ...
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### Notation for matrix and sum of matrix rows

I have a table that describes the influence of sources (columns) on sinks (rows) where rows=$(A,B,C)$ and columns=$(A,B,C,D,E)$. So my table looks like: ...
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### 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 ...
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### Basic matrice notation

I want to compute the L2 distance between a set of points X and M using matrices, for that I proceed as follows: 1) I substract both matrices, X-M 2) I square each matrice member (X-M)^2 3) I ...
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### Column or row of a matrix?

The question is so simple, but I cannot find the answer. Is $M_i$ (usually) the $i^{\text{th}}$ column of matrix $M$? Or the $i^{\text{th}}$ row? Since $M_{ij}$ is the $j^{\text{th}}$ element of the ...
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### $\mathbb{R}_*$ Notation

What does the notation $\mathbb{R}_*$ denote? I am seeing it used for showing domain of matrices, $M\in \mathbb{R}_*^{a \times b}$, which is different from $N \in \mathbb{R}^{a \times b}$. But I do ...
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### Notation in Linear Algebra

What does $(A\mid b)$ denote in Linear Algebra? Specifically in the context of the following question: "If $(A\mid b)$ is in reduced row echelon form, prove that A is also in reduced row echelon ...
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### Is there a way in matrix math notation to show the 'flip up-down', and 'flip left-right' of a matrix?

Title says it all - is there an accepted mathematical way in matrix notation to show those operations on a matrix? Thanks.
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### problems on define set with polynomials

I'm trying to say set A is the set of nonnegative integers that not of this two forms $3x^2 + (6y-4)x - y\$ and $\ 3x^2 + (6y-2)x + (y - 1)$, for example: $4=3 \cdot1^2+(6 \cdot1-4) \cdot 1-1\$ is ...
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### Notation for appending 2 submatrices

I have a matrix $M$ with $i$ rows and $(e+n)$ columns: $M_{i,e+n}$ I would like to express that $M_{i,e+n}$ is the result of appending $M_{i,e}$ and $M_{i,n}$ What is the algebraic notation to ...
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### Question about notation matrix of partial derivatives where one component has two indices

lets suppose we have a vector ($\delta_{11}, \delta_{12}, \dots, \delta_{jk}$) where $\delta_{jk} = \alpha_j + \beta_k$, i.e., each element is build up of two components. The first index $j$ specifies ...
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### Looking for notation of set of all entries of some matrix?

I'm busy writing my thesis, and I'm looking for some concise notation to denote the supremum of the matrix entries of, say $A \in M_n(\mathbb{R})$. How should I do this? Looking for something like ...
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### Notation - Transpose of Block Matrices [Lay P121 Q2.4.12]

Definition of Transpose is $(A^T)_{ij} = A_{ji}$ $1.$ Why $\begin{bmatrix} M & N \end{bmatrix}^T = \begin{bmatrix} M^T \\ N^T \end{bmatrix}$, and NOT $\begin{bmatrix} M \\ N\end{bmatrix}$? ...
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### Matrix Mathematical Notation

I am trying to work out the mathematical notation for combining the columns of two matrices, $$A=\begin{pmatrix}1 & 3 & 5 \\ 2 & 4 & 1 \\ 3 & 7 & 9\end{pmatrix}$$ and ...
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### What is the Δ above the = symbol?

I am reading this and at equation 4.21 it has an equal symbol with a Δ above it. Do you know how this is called, and what it does? Thanks
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### How to define a set for a matrix

I have a big matrix and I have partitioned it. So, I want to say that I am taking the summation of entries that do not belong to the blocks in the diagonal. How can I say it mathematically. Is it ...
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### What is this form of 'notation' called?

I was reading some of Max Tegmark's lecture materials and I found this little thing. Is there a name for it? Specifically, I am talking about $S_1$ R $S_2$ & $S_1$ R $S_2$ and the matrix. Is ...
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### A question regarding notation of equation

I'm reading a research paper, and, have come across this summation equation $$S_{2} = \sum_{N -1}^{j = 0}w_{j}^{2}\cdot$$ My question is: if j = 0..... N-1 do I ...
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### Notation for summing all elements under the diagonal of a square matrix

I have a simple question: What is the notation for summing all elements under the diagonal of a square matrix? I appreciate your help.
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### Notation for Kronecker product of a matrix and itself?

What is the notation for the Kronecker product of a matrix and itself? In other words, is there a short-hand way I can express the following: $X⊗X$ $X⊗X⊗X$ $X⊗X⊗X⊗X$ Where $X$ is a matrix? What ...
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### Basic question: what does the notation $[A,B]$ mean?

If $A$ and $B$ are both matrices, what is $[A,B]$? I understand that it is a commutator and that $[A,B]=AB-BA$, but since I don't know what a commutator is, none of this information is telling me ...
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### Aggregating a vector of $1\times K$ into a vector $1\times J$, such as $J<K$

I am stuck with a matrix algebra operation: how do I do (and mainly which notation to use) to aggregate the numbers of a vector $1\times K$ into a vector of $1\times J$, such as $J$ is of course lower ...
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### Notation for the set of symmetric matrices and symmetric positive definite matrices

I would like to know if there exists a notation for the set of symmetric matrices and symmetric positive definite matrices. For instance, the set of $N \times N$ matrices with real entries is denoted ...
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### Alternate convention in matrix multiplication?

I'm going through Halmos's Finite-Dimensional Vectorspaces. I noticed an oddity in a proof where the indexes seemed to be swapped when multiplying a matrix by a vector. I went back about 30 pages to ...
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### What is the modern use of $\bigodot$ sign?

I've seen $\bigodot$ used in various contexts. It's used for a special set theory operation by some authors (say, Saks) and as sign for Hadamard product by a couple other authors (say, Wiener) in the ...
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### Matrix notation: Does empty space means a bunch of zeros?

I don't understand what is meant with the following notation: I think this means that the first row = 4 2 0 ... 0 second row = 1 4 1 0 ... 0 third row = 0 1 4 1 0 .. 0 etc. Is this correct ?