hello, what's the essential role of a determinant for a matrix? my book says it's mainly to find if a matrix is invertible but is that it? surely there's a more important result?
thank you
#determinant of a matrix
grizzled wolf
hot bridgeBOT
cold crown
The easiest way to interpret the determinant is that it shows how much volumes get scaled
little owl
It can also be used to solve a system of linear equations and also to check consistency of the system of linear equations. As for geometrical use it can be used to find the areas and volumes of certain shapes . it is also used for finding cross products
cold crown
If you have a matrix and interpret is as the matrix of a linear operator, then its determinant shows how much the (n-dimensional) volume gets skewed under that operator
For example, a determinant 0 tells you that you lose at least one dimension and so the n-dimensional volume is lost (imagine projecting a 3d cube onto a plane, its 3d volume becomes 0)
frosty agate
potent tide
note that to talk about n-volumes we need a measure on the space, but to talk about determinants we don't
sterile hollow
hello, what's the essential role of a determinant for a matrix? my book says it'...
pretty much its the scale factor for change in area after a matrix transformation
steep idol
