Shortcut to find if a matrix (nxn) is singular or not?

[dlevanchuk]

Is there a quick shortcut to find if a matrix (nxn) is singular or not?

For example, if the matrix is (2x2), and \Delta (i.e. ad-bc) = 0, then matrx is singular and irrevertable..

Is there something similar for (nxn), like (3x3) and (100, 100), without doing the linear independence?

 

[radou]

There are different ways to see if a matrix is singular or not, but all of them requires some calculation, as far as I know.

 

[dlevanchuk]

then what would be the fastest way to check the singularity of matrix?

lets say my (3x3) matrix is A = [1 2 3; 1 3 2; 1 1 4]. Obviously, if we set Ax = 0, and do G/J elimination we find that this particular matrix is singular... but, man! It takes forever haha.

 

[radou]

Try to find its eigenvalues - if one of them is 0, then A is singular.

 

[Rasalhague]

Is there a quick shortcut to find if a matrix (nxn) is singular or not?

For example, if the matrix is (2x2), and \Delta (i.e. ad-bc) = 0, then matrx is singular and irrevertable..

Is there something similar for (nxn), like (3x3) and (100, 100), without doing the linear independence?

Yes, it's called the determinant, but it's not practical to do by hand for big matrices. Luckily there are computers...

http://www.wolframalpha.com/input/?i=det{{1%2C+2%2C+3}%2C+{1%2C+3%2C+2}%2C+{1%2C+1%2C+4}}