As I am reviewing my notes for my controls class I finally have grown tired of not knowing what all of the math is really describing. Being able to memorize mathematical mechanics to find the solution to a homework problem is not the definition of truly understanding the problem. Yet a true understanding is what actually provides value, otherwise I'm just a really slow, lame computer. I've got a long way to go it seems, but my first step was to determine what a determinant is. I have found some pretty decent descriptions online and just wanted to log my favorite here for safe keeping.
Original Question:
> Hi all,
> Can somebody tell me the physical significance of the following:
> 1. Determinant of a matrix
> 2. Rank of a matrix
> Thanks,
> Maya.
Response:
The determinant of a 3x3 matrix is the volume (up to sign) of a cardboard
box with edgevectors as rows (or columns). The rank of the same matrix
tells you, whether those vectors give you a "real" box (when rank is 3).
If the rank is only two, then the cardboard box has been run over by a
steamroller. If the rank is only one, then the box is compressed into
a line. Finally, if the rank is zero, then your box consists of a single
point.
Cheers,
Jyrki Lahtonen, Turku, Finland
That's a double whammy as I also have a better feel for the rank of a matrix.
Later,
Matt
Original Question:
> Hi all,
> Can somebody tell me the physical significance of the following:
> 1. Determinant of a matrix
> 2. Rank of a matrix
> Thanks,
> Maya.
Response:
The determinant of a 3x3 matrix is the volume (up to sign) of a cardboard
box with edgevectors as rows (or columns). The rank of the same matrix
tells you, whether those vectors give you a "real" box (when rank is 3).
If the rank is only two, then the cardboard box has been run over by a
steamroller. If the rank is only one, then the box is compressed into
a line. Finally, if the rank is zero, then your box consists of a single
point.
Cheers,
Jyrki Lahtonen, Turku, Finland
That's a double whammy as I also have a better feel for the rank of a matrix.
Later,
Matt