Matrix feature value, feature value, and Singular Value

A matrix A acts as a constant, and the result is only equivalent to multiplying the vector by a constant λ. That is, if a * A = λ A, A is the feature vector of matrix A, and λ is the feature value of matrix. The scalar value is the same as that of the feature vector in terms of quantum mechanics. However, this value is not limited to matrices, but also meaningful to differential operators. The function of a differential operator A is equivalent to that of the Function x a constant λ. That is, a psi = λ PSI, then PSI is the intrinsic function of the differential operator A, and λ is the intrinsic value of the differential operator. Singular Values can be decomposed into a = usv for a real matrix A (Order m × n), where U and V are orthogonal arrays of order m × n and n × m, respectively, S is a rank n x n diagonal matrix, and S = diag (A1, A2 ,..., ar, 0 ,..., 0 ). A1> = A2> = A3> =...> = ar> = 0. So A1, A2,..., Ar is called the singular value of matrix. U and V are left and right singular arrays. The singular value of A is the square root of the feature value of a' A (a' represents the transpose matrix of a). Here, the singular value can be obtained.