Sentence examples for using the characteristic polynomial from inspiring English sources

We consider the (( k ) times ( 2k ) ) Jordan-type matrix J which is defined by using the characteristic polynomial of the k-step Fibonacci sequence: begin{bmatrix} 1 & -1 & -1 & ldots& -1 & 0 & 0 & ldots& 0 0 & 1 & -1 & ldots& -1 & -1 & 0 & ldots& 0 vdots& & ddots& ddots& & & & & 0 & ldots& 0 & 1 & -1 & -1 & -1 & ldots& -1 end{bmatrix}.

Natural frequencies and modes are obtained applying the assumed mode method using the characteristic polynomials of a Timoshenko beam.

Using a property of the characteristic polynomial coefficients of a matrix and the well-known Routh–Hurwitz criterion in control engineering, it is shown that under certain conditions, the response of a Hessian-based enhancement filter to an image element can be obtained without having to compute Hessian eigenvalues.

Our server uses the Quaternion Characteristic Polynomial (QCP) method recently proposed by [ 24].

In order to calculate the eigenvalues of the matrix that appears at the quadratic form of the metric, the definition of the characteristic polynomial is used: det I - σ w 2 Λ 1 / 2 U H Σ y - 1 C - 1 Σ y - 1 U Λ 1 / 2 - χ I = det σ w 2 Λ 1 / 2 U H Σ y - 1 C - 1 Σ y - 1 U Λ 1 / 2 + χ - 1 I = det Λ det σ w 2 Σ y - 1 C - 1 Σ y - 1 + χ - 1 C - 1 = 0 (47).

More specifically, we provide the first efficiently and verifiably secure outsourcing protocol for the computation of the characteristic polynomial and eigenvalues by using disguising technology.

We exploit the symmetry of the resulting equations to factor the characteristic polynomial into the product of two cubic polynomials and then use the Routh–Hurwitz criteria.

In this paper, we use data hiding technique to design a secure and verifiable outsourcing protocol for computing the characteristic polynomial and eigenvalues of a matrix.

(The determinant of is also often written.) In linear algebra, the polynomial is called the characteristic polynomial for the matrix.

The roots of the characteristic polynomial are called the eigenvalues of.

The characteristic polynomial factors.