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


1 Answer 1


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.

  • $\begingroup$ 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 $\endgroup$ Dec 12, 2013 at 6:00

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