I know how to solve for the determinant of a matrix, but I'm struggling to understand what it represents.
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Rather, see this classic thread: http://math.stackexchange.com/questions/668/whatsanintuitivewaytothinkaboutthedeterminant – Travis Willse May 09 '15 at 09:07
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A nice intuitive visualization is: The determinant is the (oriented) $n$dimensional volume of the epiped ("distorted cube") spanned by the column vectors. Especially, the deteminant is zero iff the epiped is "squashed" to lower dimensions, i.e., iff the matrix is not invertible.
Hagen von Eitzen
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