Many applications
What do vectors and vector spaces bring us beyond a presence, like all mathematical structures, a little everywhere around us? An opening and an enrichment of our approach to many fields, illustrated by some striking examples, where this change has operated a real revolution, accentuated by the advent of powerful calculation tools! Vector drawing in graphics, the enormous amounts of texts or corpora in literature… And Yannis Xenakis in person even opened the way to interesting vector techniques in musical composition…
All articles in this folder
Words are vectors!
Comparing two vectors is rather like comparing two texts. This analogy proves highly relevant to the study of a literary corpus: combined with computing power, the tools of linear algebra can be used to compare two texts or measure their similarity.
Drawing a spider's web
Have you ever found yourself doodling spiderwebs in the margin of a calculation that was going nowhere? Not like an entomologist (since spiders are not insects), but however you please, subject to a few simple geometric rules...
Polynomials... viewed as vectors
What could a quadratic polynomial possibly have in common with a vector in three-dimensional space? At first glance, nothing: they are different kinds of objects. Yet both have the same form—each is described by a triple of numbers. Better still, calculations with one correspond to calculations with the other!
Linear equations and linear recurrences are one and the same!
One of a mathematician's skills is recognizing the same structures in different guises. A similarity in the calculations used in two ostensibly separate areas is often an early sign of this… Let's look at certain differential equations and sequences.
Gram–Schmidt method – Math brief | Tangente
Discover the celebrated Gram–Schmidt method for constructing orthonormal bases of vector spaces
Drawing a line: not so simple! – Maths brief | Tangente
How can straight lines be drawn on a screen made up of pixels? Several algorithms can solve this thorny problem.
The vector art manifesto – Maths brief | Tangente
The Scowcza collective creates works of vector art. You have already come across several of them in the articles in this issue
Matrix algebra in our images – Maths brief | Tangente
Matrices and vectors have become indispensable mathematical and computational tools for digital image processing.
Yannis Xenakis's "musical vector spaces" | Tangente
In 1963, the celebrated composer Yannis Xenakis introduced a kind of arithmetic for musical composition, based on the notion of mathematical structure—in particular, that of a vector space. This artistic contribution lends itself wonderfully to scientific analysis.