Revision as of 00:29, 20 April 2025 by Bot (Created page with "<div class="d-none"><math> \newcommand{\mathds}{\mathbb}</math></div>Prove with full details, based on the above, that the determinant of the systems of vectors <math display="block"> \det:\mathbb R^N\times\ldots\times\mathbb R^N\to\mathbb R </math> is multilinear, alternate and unital, and unique with these properties. Then try to prove as well this directly, without any reference to geometry.")
BBot
Apr 20'25
Exercise
[math]
\newcommand{\mathds}{\mathbb}[/math]
Prove with full details, based on the above, that the determinant of the systems of vectors
[[math]]
\det:\mathbb R^N\times\ldots\times\mathbb R^N\to\mathbb R
[[/math]]
is multilinear, alternate and unital, and unique with these properties. Then try to prove as well this directly, without any reference to geometry.