# Tagged Questions

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### Cayley on “trivial transformations”

In his 1854 paper, "Deuxième mémoire sur les fonctions doublement périodiques" ("Second memoir on doubly periodic functions"), Cayley discusses (what we would today describe as) a certain class of ...
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### Why is the permanent of interest for complexity theorists?

Studying a bit about the determinant and the permanent, I'm told that although both concepts have very similar formulas, the permanent was of not much interest historically - it was until later that ...
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### Origin of the modern definition of the tensor product

Due to whom is the modern (i.e. via its universal property) definition of the tensor product, and in which article was it communicated?
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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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### Cauchy Schwarz Inequality Original Reference

The inequality is well known to experts in linear algebra and computational geometry. However, I want to know the original source of the inequality (in the form of a published journal article, if ...
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### What is the mathematical intuition behind àl-jàbrà?

The term algebra comes from the arabic term àl-jàbrà 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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### Why the SVD is named so…

The SVD stands for Singular Value Decomposition. After decomposing a data matrix X using SVD, it results three matrices, two singular vactors U and V, and one singular value matrix whose diagonal ...
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### Why cross product's formulas defined in this way? [closed]

Why cross product's formulas defined in this way? When mathematicians need to define cross product?
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### Why is the Leibniz formula for determinants called such?

My professor said that Leibniz was not even aware of the concept. The Wikipedia page says that the formula was named "in honor of Gottfried Leibniz." What gives? Did he do work that was related, and ...
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### Why, historically, do we multiply matrices as we do?

Multiplication of matrices — taking the dot product of the $i$th row of the first matrix and the $j$th column of the second to yield the $ij$th entry of the product — is not a very ...
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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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### Who was the first to use dual space?

Who was the first person who used the dual space? In which paper / book did he or she use the dual space? Who was the first who called it dual space and in which paper / book?
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### The contributions of James Sylvester to linear algebra.

The claim is James Sylvester and Arthur Cayley are the fathers of Linear Algebra. I can find the various parts that Cayley contributed to Linear Algebra, but there is not much on the contributions ...
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### References on the History of Linear Algebra

I have an aggregated understanding of the history of linear algebra compiled from friends, teachers, and coworkers. It may have several errors. It goes something like this: Even ancient cultures ...
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### History of solving linear equations with matrices

I'm solving linear equations with matrices right now and I wonder, how did it start. Who, how, why came to idea that such kind of equations could be solved with matrices? What was first: matrix or ...
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### Origin of the dot and cross product?

Most questions usually just relate to what these can be used for, that's fairly obvious to me since I've been programming 3D games/simulations for a while, but I've never really understood the inner ...
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### What's the “geometry” in “geometric multiplicity”?

The geometric multiplicity of an eigenvalue is defined as the dimension of the associated eigenspace, i.e. number of linearly independent eigenvectors with that eigenvalue. Here are my questions: ...
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### History of dot product and cosine

The fact that the dot product and the cosine of the angle between two vectors are mutually computable is easy to show (see the two sides in the two answers at Dot product in coordinates). But looking ...