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Questions tagged [linear-algebra]

For questions about linear algebra, a mathematical field studying vector spaces and matrices.

2
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1answer
38 views

Jordan's Paper on the Jordan Canonical Form

In which paper, did Jordan introduce/prove the Jordan canonical form?
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1answer
83 views

How to understand `After quantum mechanics, nature itself suddenly became linear`?

How to understand Freeman Dyson's Saying: After quantum mechanics, nature itself suddenly became linear.
4
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1answer
151 views

First appearance of tensor product symbol $\otimes$

I was asked recently if the tensor product symbol $\otimes$ had been used before Bourbaki's publication on multilinear algebra in 1948 (a draft of this document can be seen at http://sites.mathdoc.fr/...
0
votes
1answer
67 views

Invention of matrix symbols

Who first did use the symbol $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ for a matrix and similarly $\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$? Why do these two ...
2
votes
2answers
147 views

Where did block matrix multiplication appear?

I am curious about who first noticed that block matrices can be multiplied blockwise. There is a section about matrices partitioned into submatrices that describes block matrix multiplication in "An ...
3
votes
1answer
171 views

Why is the term “kernel” used in algebra? [duplicate]

What was the motivation to use the word "kernel" in algebra to denote the set of all arguments which are mapped to the idendity element (by a homomorphism)? Who introduced it?
4
votes
1answer
158 views

Binet-Cauchy or Cauchy-Binet?

The Cauchy-Binet formula in linear algebra gives the determinant of a square matrix $AB$ for rectangular matrices $A,B$ of appropriate shape in terms of the determinants of the submatrices of $A,B$. (...
4
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3answers
445 views

Motivation for the development of modern linear algebra

In many text books on linear algebra one of the most important applications is geometry in Euclidean spaces and therefore there seems to be the impression that linear algebra was developed in order to ...
5
votes
1answer
362 views

Where does the name eigenvalue come from?

Who introduced the concept of eigenvalues and eigenvectors and where does the name come from? Is there a connection with the German word "eigen"?
2
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2answers
258 views

Grassmann Formula

I'm in my first year of Mathematics at the University. Recently, we've learnt about Grassmann Formula and when I was making a little research on the internet, I couldn't find a single reference ...
4
votes
2answers
281 views

Who discovered the Jordan normal form?

In the paper by A. J. Coleman, "The greatest mathematical paper of all time", (Math Inteligencer, 11, 3 (1989) 29-39, on page 30 there is a passing remark that the "Jordan form is due to Weierstrass". ...
7
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5answers
272 views

Were matrix theory and functional analysis well-known to physicists before the invention of matrix mechanics?

Were matrix theory and analysis well-known to physicists circa 1920-1925? Did physicists make extended use of this theory in that period? The question is related to the discussion in How did ...
0
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0answers
114 views

What questions led Cayley to the definition of matrix multiplication?

quote: every book I've seen on matrix algebra or linear algebra seem[s] to just define the matrix operations without providing any historical background Talk:Matrix multiplication - Wikipedia, the ...
5
votes
1answer
194 views

How did the exterior product get its symbol?

As per the title: where did the notation $a\wedge b$ for the exterior product of $a$ and $b$ originate, and/or who popularised it? I'm especially interested in motivation for the choice of this symbol ...
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vote
0answers
158 views

Need information about the history of the Hotelling and Bodewig method

I need information about Hotelling and Bodewig, who they were and why they developed this method. anything will help, references to articles, links, or any other information. Link to the method: http:...
3
votes
2answers
474 views

The terminologies “Adjoint” and “Adjugate”

The adjoint of a matrix is also called the adjugate. However, the word "adjoint" is also used in Linear Algebra for linear transformations, and the "adjoint of a matrix" and "adjoint of a linear map"...
6
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3answers
308 views

Why do we call a linear mapping “linear mapping”?

According with the book Classic Algebra by P.M.Cohn for historical reasons we call a linear mapping "linear mapping". What are the historical reasons that created the term "linear mapping"?
11
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2answers
354 views

What came first? The kernel from vector spaces or from group theory?

In studying vector spaces we learn about linear transformations from one vector space to another and in particular the kernel of such a transformation. When learning about group theory we also learn ...
7
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1answer
783 views

History of the inverse matrix

I know the definition and the procedure to calculate the inverse of a matrix, but I want to know the history of starting the idea of an inverse matrix. mathematicians must have faced a real life ...
7
votes
1answer
283 views

Gauss accused of witchcraft: apocryphal?

I recall reading years ago in a linear algebra book that Gauss was accused of witchcraft for his (re)discovery of what we now call the row reduction algorithm for solving linear equations. Has anyone ...
15
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3answers
579 views

Books on the history of linear algebra

I'm quite desperate to understand the historical motivation and origin of all of the "geometrical" concepts of linear algebra, namely: The concept of thinking of elements of $\mathbb R^n$ or some ...