# Discriminates - for matricies greater than 3x3, or non square.

• Mar 1st 2013, 04:56 AM
zendo
Discriminates - for matricies greater than 3x3, or non square.
The other algebra forum stated that it was NOT the place for questions about Matrices that were larger than 2x2, however, this question does not really seem to belong here either, so let me apologize in advance.

That being said, my textbook, after explaining determinate, minors, and coefficients for 3x3 matrices, just drops the topic. I bet that is not the end of the story though. I'm a little curious about non-square matrices, or matrices larger than 3x3.

Does anyone know of any sources or links that I could continue along this vein?
• Mar 1st 2013, 05:45 AM
Ant
Re: Discriminates - for matricies greater than 3x3, or non square.
Quote:

Originally Posted by zendo
The other algebra forum stated that it was NOT the place for questions about Matrices that were larger than 2x2, however, this question does not really seem to belong here either, so let me apologize in advance.

That being said, my textbook, after explaining determinate, minors, and coefficients for 3x3 matrices, just drops the topic. I bet that is not the end of the story though. I'm a little curious about non-square matrices, or matrices larger than 3x3.

Does anyone know of any sources or links that I could continue along this vein?

As far as I'm aware, finding the determinant of a matrix is only defined for square matrices.

For matrices larger than 3X3, you can simply extend the process which you used for 3X3 matrices. It shouldn't be too difficult (although it can be very tedious...).

Just as for 3X3 matrices you reduced to a set of three 2X2 matrices (with coefficients), you can do the same for an nXn matrix (reducing to set of n-1Xn-1 matrices, each of which you reduce to a set of n-2Xn-2 matrices and so on untll you arrive at (many!) 2X2 matrices which you can evaluate directly). In fact, the definition of determinant is often giving inductively.
• Mar 1st 2013, 07:37 AM
zendo
Re: Discriminates - for matricies greater than 3x3, or non square.
That is very helpful. Many thanks.