T ( v ) = λ v. where λ is a scalar in the field F, known as the eigenvalue, characteristic value, or characteristic root associated with the eigenvector v. Let’s see how the equation works for the first case we saw where we scaled a square by a factor of 2 along y axis where the red vector and green vector were the eigenvectors. 2. (1) Geometrically, one thinks of a vector whose direction is unchanged by the action of A, but whose magnitude is multiplied by λ. Let A be a 3 × 3 matrix with a complex eigenvalue λ 1. The first column of A is the combination x1 C . Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … detQ(A,λ)has degree less than or equal to mnand degQ(A,λ)