2
$\begingroup$

What's the simplest way to check if a NxN Matrix determinant is zero ? Using Gauss Jordan to calculate the determinant first is to complicated (took N^3 calculation), is there any way to know it in at most (N^2 calculation).

Anyway the matrix is always in form of this (the first row is known value) :

2x2 matrix $\begin{bmatrix} a & b \\ b & a \\ \end{bmatrix}$

3x3 matrix $\begin{bmatrix} a & b & c \\ b & c & a \\ c & a & b \end{bmatrix}$

4x4 matrix $\begin{bmatrix} a & b & c & d\\ b & c & d & a\\ c & d & a & b\\ d & a & b & c \end{bmatrix}$

$\endgroup$
3
$\begingroup$

All you ever wanted to know about such matrices (including the answer to your question) can be found in this Wikipedia article about circulant matrices.

$\endgroup$
  • $\begingroup$ Thanks! but i'm not familiar with complex number, how can i calculate matrix {1,1,1},{1,1,1},{1,1,1} with that formula, i'm unable to get 0 as the determinant, can you show me an example ? thanks again $\endgroup$ – Terry Smith Dec 12 '13 at 6:00

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.