[OS X TeX] Latex symbol for "define equal"

Martin Berggren martin.berggren at cs.umu.se
Tue Aug 21 13:59:18 CEST 2018

> On 21 Aug 2018, at 13:47, Markus Klyver <markusklyver at hotmail.com> wrote:
> The thing is that you can have several different definitions, all equivalent.  Consider the definition "a matrix A \in \mathbb R^{n \times n} is invertiable iff A have a multiplicative inverse". It turns out that this is equivalent to a lot of things, among det(A) !=0, A having full rang, A having n linearindependent eigenvectors, Ax=0 only having the trivial solution, Ax=b having a solution (which is unique) for every right-hand-side b, etc.

I would save that this is a theorem, not a definition. I think of a definition as a “macro”; that is,  giving a short name to a mathematical property. Example: a matrix A is called positive semidefinite when x^T Ax \geq 0 for all vectors x. The point is that you in each instances when the name is used, it can be replaced by its definition. 


Martin Berggren
Department of Computing Science, 
UMIT Research Lab
Umeå Universitet
Campustorget 5, S-901 87 Umeå, Sweden. Ph: +46-70-732 8111
http://www.cs.umu.se/~martinb <http://www.cs.umu.se/~martinb>, Martin.Berggren at cs.umu.se <mailto:Martin.Berggren at cs.umu.se>

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