Questions tagged [linear-algebra]
For questions about linear algebra, a mathematical field studying vector spaces and matrices.
2
votes
1answer
38 views
Jordan's Paper on the Jordan Canonical Form
In which paper, did Jordan introduce/prove the Jordan canonical form?
0
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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 ...
1
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
votes
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
votes
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
votes
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
votes
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 ...
