1 and a can be expressed as α β t, where α and β are n-dimensional column vectors.

2、A^k=(α^Tβ)^(k- 1)A

3、tr(A)=α^Tβ

4. The eigenvalues of A are α t β, 0, 0, ..., 0.

Note: α t β = β t α.

Extended data

Definition of matrix with rank equal to 1;

A matrix with rank equal to 1 is a special matrix, which can be expressed as the product of a non-zero column vector (column matrix) and a non-zero row vector (row matrix). According to the associative law of matrix multiplication, the multiplication and power operation of this kind of matrix can be greatly simplified. The eigenvalues and eigenvectors of such matrices have their particularity.