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

Martin Berggren martin.berggren at cs.umu.se
Tue Aug 21 07:59:18 EDT 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.

Sincerely,

Martin Berggren
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Department of Computing Science,
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Umeå Universitet
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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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