Questions tagged [linear-algebra]

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

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6
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1answer
227 views

Origin of Tensor Product

When and why did Mathematicians saw a need to define Tensor Products? I want to know the historical development of the idea "Tensor Product"?
4
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0answers
172 views

Why did Jordan introduce his canonical form?

Camille Jordan's famous canonical form for matrices over algebraically closed fields, is considered an important result nowadays, commonly taught to all students of mathematics in undergraduate linear ...
3
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0answers
137 views

The origins of $\det(I+AB)=\det(I+BA)$

I am looking for the earliest published source that gives and perhaps proves the identity $\det(I+AB)=\det(I+BA)$ where $A$ and $B$ are just rectangular matrices of finite dimensions (as opposed to ...
2
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0answers
60 views

Origin of Lang's proof of the Cayley-Hamilton theorem

Is the proof of the Cayley-Hamilton theorem given by Serge Lang in Algebra (page 561) an original one, or has it been borrowed from some earlier sources? Who came up with it first? (Lang's proof is ...
2
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0answers
112 views

Interpretation of a short note of Gauss on the resolution of a special system of inhomogeneous linear equations by roots of unity

My question refers to a 2-pages fragment of Gauss, entitled: "Note on the resolution of a special system of linear equations", which is found on pages 30-31 of volume 8 of his works. In this ...
1
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0answers
64 views

Why are linear forms called “forms”?

My question is about linear forms, quadratic forms, n-linear forms, differential forms and so on. The first term of these names seem clear to me, but I cannot make a link between these mathematical ...
1
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0answers
64 views

Research about Stafford Beer's claim about a method for solving simultaneous equations unknowingly via a game by kids?

I found this claim in the book "How many grapes went into the wine", in the Artorga section: In 1956 I devised a game for solving simultaneous linear equations in two variables. The theory ...
1
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0answers
277 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:...
0
votes
0answers
69 views

What is the earliest article in which Leibniz used 'matrices'?

The Chinese were using matrices ( fengcheng in the Nine Chapters of the Mathematical Art), long before they were used in Europe which suggests that possibly they were introduced by way of them. For ...
0
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0answers
177 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 ...