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A vector x perpendicular to the plane has Px = 0, so this is an eigenvector with eigenvalue λ = 0. (1) Geometrically, one thinks of a vector whose direction is unchanged by the action of A, but whose magnitude is multiplied by λ. determinant is 1. The dimension of the λ-eigenspace of A is equal to the number of free variables in the system of equations (A-λ I n) v = 0, which is the number of columns of A-λ I n without pivots. detQ(A,λ)has degree less than or equal to mnand degQ(A,λ)

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