# Tagged Questions

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I have converted from an individual-level adjacency matrix to one for clusters and I am trying to show mathematically how I programmed up determining the mean number of inter-cluster links. I am not ...
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### Is there any distinction between these products: scalar, dot, inner?

I hope you will forgive a math question that comes up in physics contexts where language is loose. This question migrated from Physics SE. I'm finding that I sometimes don't know what kind of product ...
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### Is there a traditional name for the “eigenspace” function?

Let $A$ denote a field, $X$ denote an $A$-vector spaces, and suppose $\varphi : X \rightarrow X$ is a linear transformation. Is there a traditional name for the corresponding "eigenspace" function? By ...
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### I need help understanding what r-th and s-th rows are.

Let E be the matrix obtained from the unit $n \times n$ matrix by multiplying the $r$-th row with a number $c$ and adding it to the $s$-th row, $r \neq s$. Let $A$ be an $n \neq n$ matrix. Then ...
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### Terminology of “linear”, “quadratic”, etc. for multi-input functions

It is my understanding that, according to typical math terminology: The function $f(x, y) = x + y$ is "linear". Specifically, it's linear in both $x$ and $y$, but this is understood implicitly. ...
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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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### What is a “component function” of a matrix that is a linear map?

The matrix is: $$\pmatrix{ 1&2\\ 3&4}$$ and this matrix is an $\Bbb R^2 \to \Bbb R^2$ linear map. I am asked to explicitly write the component functions of $A$. What does "component ...
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### What does the term “distinguished basis” mean?

I know what a basis is (talking about vector spaces here), but I don't know what a distinguished basis is. Can you please explain the difference to me? I did not grow up in an English-speaking ...
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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 is the difference between a point and a vector

I understand that a vector has direction and magnitude whereas a point doesn't. However, the course note that I am using states that a point is the same as a vector. Also, can you do cross product ...
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### In the context of vectors is there a difference between the terms “magnitude” and “length”?

I noticed vectors are usually said to have "length and direction" but then it is said that people want to find the "magnitude". Is this just a difference in terminology or is there something more to ...
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### Fundamental theorem of linear algebra

When I studied linear algebra we (our books, our professors) used to call Fundamental theorem of linear algebra the theorem that says: Fundamental theorem of linear algebra: A linear ...
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### Adjoint of a Matrix Definition

Tom M. Apostol in his book "calculus Vol. 2" page 122 (see image below) defines adjoint of a matrix as the transpose of the conjugate of the matrix. Is this definition always correct ? Does it agree ...
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### A name for a linear map from primary to dual space

Is there a standard name for a linear function $f:\mathbb R^n\to(\mathbb R^n)^*$ defined on the standard basis $e_i, i=1,\dotsc, n,$ of $\mathbb R^n$ by $f(e_i)=e^i$, where $e^i, i=1,\dotsc,n,$ is the ...
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### Is there an object which groups two vectors together?

Is there a single name for a pair of vectors that together describe a position and orientation? Like an "oriented point" or something like that?
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### Minimal Spanning Set vs Basis of a vector space

I read the following in my textbook: Find as small a set of vectors that span the row space of $A$ as you can. Such a set is called a minimal spanning set. Is this terminology synonymous with ...
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### Support of a vector

What is the support of a signed vector? By signed vector, I mean a vector which is determined by considering the signs of the coefficients of the entries of another vector.
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### What's $\{x\in V|\exists p\in \mathbb{Z}^+ {\phi(T)}^p(x)=0\}$ called?

I'm studying rational canonical form right now. Let $\phi(X)$ be a irreducible monic polynomial in $F[X]$ and $T$ be a linear operator on a vector space $V$ over $F$, where $F$ is a field. Define ...
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### What is the mathematical intuition behind àl-jàbrà?

The term algebra comes from the arabic term Ã l-jÃ brÃ  that means "to force", "to restore". Over centuries mathematicians, in east and west, celebrate by this term mathematical disciplines. What is ...
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### Is LinearTransformation's matrix a square matrix?

Linear Transformationâ€™s confusions. Is linear transformation's matrix a square matrix? Some books define linear transformation is $V\to W$, and say linear operator is $V\to V$. Some books define ...
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### What is a “rotated” basis?

My text (p. 19) introduces the concept of a "rotated" basis without explanation. What properties or characteristics of a basis make it "rotated" with respect to another? What operation on one basis ...
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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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### Why are vector spaces sometimes called linear spaces?

I have never come across the term 'linear space' as a synonym for 'vector space' and it seems from the book I am using (Linear Algebra by Kostrikin and Manin) that the term linear space is more ...
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### Simple linear operator?

From Wikipedia a linear operator T on a finite-dimensional vector space is semi-simple if every T-invariant subspace has a complementary T-invariant subspace. I wonder if there is a concept for ...
What is the difference, if any, between kernel and null space? I previously understood the kernel to be of a linear map and the null space to be of a matrix: i.e., for any linear map $f : V \to W$, ...