# Tagged Questions

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### About matrix $R$, what is this called: $R^TR$? What is it for?

I am doing singular value decomposition on a matrix $R$. The first step is to compute such a matrix $R^TR$. What is this matrix? A reference told me this is cross product of matrix R. I use a ...
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### Matrices and what they represent

I know matrices can represent transformations but they can also represent the points that are transformed by another matrix do these two types have different names and if so what are they?? thanks
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### Whats the name of this sort of matrix

What the name of such a matrix \begin{pmatrix} 1 & 2 & 5 & 10 \\ 3 & 4 & 7 & 12 \\ 6 & 8 & 9 & 14 \\ 11 & 13 & 15 & 16\\ \end{pmatrix} Its properties ...
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### Name for multiples of orthogonal matrices

Is there a name for a matrix which is a multiple of an orthogonal matrix? I.e. a square matrix $A$ which satisfies the condition $$A^TA = AA^T = \lambda I$$ where $\lambda$ is some scalar (which ...
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### Line in vector form?

Given the line y=3x my book states it is $\left(\begin{array}{c}1 \\ 3\\\end{array}\right)$ as a matrix. Why is it not $\left(\begin{array}{c}3 \\ 1\\\end{array}\right)$, I thought the upper number ...
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### Why is an orthogonal matrix called orthogonal?

I know a square matrix is called orthogonal if its rows (and columns) are pairwise orthonormal But is there a deeper reason for this, or is it only an historical reason? I find it is very confusing ...
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### What are matrix coefficients in linear algebra?

What are matrix coefficients in linear algebra? And what does it mean "integer matrix coefficients"?
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### Abbreviations in Combinatorial Graph/Matrix theory

I'm getting started with research in combinatorics. I have come across a reference that uses a great deal of abbreviations. I was able to figure most of them out but there are a few that I can find. ...
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### What is a Jordan Cell?

Google has been surprisingly unhelpful for me. A homework problem from my algebra class asks me to Calculate p(A) where A is a Jordan cell and p is a polynomial. ...
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### Name for diagonals of a matrix

I am looking for the terms to use for particular types of diagonals in two dimensional matrices. I have heard the longest diagonal, from top-left element and in the direction down-right often called ...
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### Name of a particular matrix close to projection

I am wondering if there is a special name for an $m\times n$ matrix $A=(a_{i,j})$, with $a_{i,j}\in\{0,1\}$ that will pick $m$ unique components from a vector $v\in\mathbb{R}^n$ ($m\le n$), it is ...
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### Names for special submatrices?

Let $(a_{ij}), i,j \in \{1,...,n\}$ be a matrix. What are the names for the following special square submatrices: for any set of indices $JâŠ‚{1,2,..,n}$, the submatrix $(a_{jk})j,k\in J$, a ...
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### Correct name for multi-dimensional array/matrix/tensor

What is the correct name for an n-dimensional array in mathematics? I have seen the following: nD-Matrix nD-Array nD-Tensor Which is the right way?
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### In 3D: column major, row major, … major?

If we use column and row major to describe dimension-majority for x and y respectively, what word is commonly used (if any) to describe such majority for the z dimension?
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### Standard terminology for the relation between $A$ and $B$ if $B= Q^t A P$?

Let $A,B$ be two rectangular $m\times n$ matrices related by $$B= Q^t A P$$ with $P$ an $n\times n$ and $Q$ an $m\times m$ matrix. Is there a standard terminolgy for this relation? If instead of ...
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### Relation between Interior Product, Inner Product, Exterior Product, Outer Product..

Following my previous question Relation between cross-product and outer product where I learnt that the Exterior Product generalises the Cross Product whereas the Inner Product generalises the Dot ...
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### Relation between cross-product and outer product

If inner products ($V$) are generalisations of dot products ($\mathbb{R}^n$), then are outer products ($V$) also related to cross-products ($\mathbb{R}^3$) in some way? A quick search reveals that ...
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### Does “nullity” have a potentially conflicting or confusing usage?

In Linear Algebra and Its Applications, David Lay writes, "the dimension of the null space is sometimes called the nullity of A, though we will not use the term." He then goes on to specify "The Rank ...
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### Generalization of the matrix concept

It has been some time since I left university... In a not too formal language, an $n$-dimensional vector is an indexed set of numbers $\{i_1, ..., i_n\}$. A $n\times m$ matrix is a set of numbers ...
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### Semigroups of matrices with zeroes and a single 1

I stumbled upon this while reviewing a Harvard lecture on abstract algebra. What I want to know is if these semigroups are known and, if so, what they are called. I've checked the assertions below for ...
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### Matrices of Trace $0$

The set of all $n$-square matrices with trace $0$ is a subspace of the set of all $n$-square matrices. Is there a standard notation and/or name for this subspace?
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### What is generic rank?

What is meant by generic rank of a matrix? Is it something different from the rank, and does the word generic has just its English meaning? I came across this term in the book "Algebraic statistics ...
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### Is there a term for the “opposite” location in a matrix?

I'm just looking for the correct term to describe a concept: Suppose I have a 5x5 matrix: A B C D E F G H I J K L M N O P Q R S T U V W X Y I can pick any two cells, let's say the cells I and Q, ...