2
votes
0answers
22 views

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 ...
8
votes
1answer
284 views

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 ...
5
votes
2answers
258 views

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?
2
votes
2answers
314 views

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 ...
1
vote
2answers
51 views

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 ...
1
vote
1answer
120 views

Historical reason to define a matrix vector product the way it is

What is the reason why we defined a matrix vector product (a transformation) this way: $$\begin{pmatrix} a_1 & a_2 \\ a_3 & a_4 \\ \end{pmatrix}\cdot ...
2
votes
1answer
133 views

Historical meaning of determinant

Some time ago, I published the following question Geometric meaning of the determinant of a matrix on the geometric meaning of determinant. Usually, on the books of algebra, the determinant is ...
25
votes
2answers
1k views

Word origin / meaning of 'kernel' in linear algebra

It may be the dumbest question ever asked on math.SE, but... Given a real matrix $\mathbf A\in\mathbb R^{m\times n}$, the column space is defined as $$C(\mathbf A) = \{\mathbf A \mathbf x : ...
12
votes
2answers
621 views

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 ...
5
votes
2answers
154 views

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 ...
-3
votes
2answers
151 views

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?
2
votes
2answers
200 views

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 ...
30
votes
3answers
2k views

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 ...
4
votes
1answer
2k views

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 ...
14
votes
2answers
377 views

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?
5
votes
4answers
767 views

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 ...
3
votes
1answer
593 views

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 ...
0
votes
1answer
613 views

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 ...
16
votes
4answers
3k views

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 ...
6
votes
2answers
305 views

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: ...
14
votes
2answers
2k views

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 ...
3
votes
1answer
877 views

What does matrix multiplication have to do with scalar multiplication?

Why are matrix and scalar multiplication denoted the same way and treated as the same operation in standard mathematical notation? This is always a source of confusion for me because they have ...
3
votes
3answers
2k views

What is Modern Mathematics? Is this an exact concept with a clear meaning? [closed]

Motivated by this question I would like to know whether there is an exact definition of modern mathematics. In which point in time (century, decade) does one think, when speaking about modern ...