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Results tagged with linear-algebra
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user 55
For questions about linear algebra, a mathematical field studying vector spaces and matrices.
7
votes
Accepted
How and by whom was the concept of generalized eigenvectors developed?
This is somewhat difficult to track because much of the work on linear algebra in 19th century was coached in the language of anything but matrices and vectors, differential equations, substitutions, …
- 80k
5
votes
Accepted
What came first? The kernel from vector spaces or from group theory?
According to an entry attributed to John Aldrich in Jeff Miller's Earliest Known Uses of Some of the Words of Mathematics, the word "kernel" in the algebraic sense was first used in the 1946 translati …
- 80k
14
votes
Accepted
What was the role of Schmidt in derivation of the Gram-Schmidt process?
A detailed history can be found in Gram-Schmidt orthogonalization: 100 years and more by Leon, Björck and Gander, see also their slides for a brief version. In short, Schmidt's 1907 presentation was m …
- 80k
5
votes
Accepted
Binet-Cauchy or Cauchy-Binet?
I am not sure what the editors of Wikipedia had in mind when arranging the names (if anything). Linear algebra textbook authors have them arranged every which way for both the formula and the identity …
- 80k
5
votes
Accepted
How did the exterior product get its symbol?
Cajori gives the early uses of logical symbols in volume 2 of History of Mathematical Notations. Neither Boole nor Schröder used $\wedge$ and $\vee$ in Boolean algebra, but rather $\cdot$ (or blank) a …
- 80k
7
votes
Accepted
Were matrix theory and functional analysis well-known to physicists before the invention of ...
One can probably say that the relevant parts of algebra were "known to experts", rather than "well-known", and the relevant parts of functional analysis did not exist at the time, see Moore's Axiomati …
- 80k
2
votes
Accepted
Why positive definite matrix rather than positively definite matrix?
According to Miller's Earliest Known Uses positive definite, as applied to forms, appears first in Pierpont's Lectures On The Theory Of Functions Of Real Variables (1905). Pierpont uses the reversed e …
- 80k
15
votes
Accepted
Who started calling the matrix multiplication "multiplication"?
The same person who introduced it, Cayley. Sylvester first used the term "matrix" (womb in Latin) for an array of numbers in 1848, but did not do much with it. Cayley started developing matrix algebra …
- 80k
10
votes
Accepted
Who invented the gradient descent algorithm?
The "gradient descent" algorithm was invented before the gradient. It is described in equivalent form by Cauchy in a 3-page paper in Comptes Rendus, Méthode générale pour la résolution des systèmes d' …
- 80k
5
votes
Accepted
Why is the term "isotropic" used to describe a quadratic form and a vector?
This is an example of how a term migrates from the original context by broken telephone through various generalizations and transfers. It started with Poncelet introducing "imaginaries", i.e. complex …
- 80k
4
votes
Accepted
Have orthogonal complex matrices appeared in the literature?
They did. A natural way to treat such matrices is to introduce an indefinite inner product on $\mathbb{C}^n$, a non-degenerate bilinear form $(z,w):=z_1w_1+z_2w_2+\dots z_nw_n$, instead of the usual s …
- 80k
3
votes
Accepted
Why is Einstein summation named after Einstein?
Einstein proposed the convention in Die Grundlage der allgemeinen Relativitätstheorie (Annalen der Physik, 354 (1916) no.7, 769-822). It is introduced on p.158 of its English translation. Einstein's s …
- 80k