Matematika Pertemuan 24 Matakuliah: D0024/Matematika Industri II Tahun : 2008

Bina Nusantara Nilai Eigen dan Vektor Eigen Let be a linear transformation represented by a matrix. If there is a vector such thatlinear transformationmatrixvector for some scalar, then is called the eigenvalue of with corresponding (right) eigenvector.scalareigenvector Letting be a square matrixsquare matrix (2) (2) with eigenvalue, then the corresponding eigenvectors satisfyeigenvectors

Bina Nusantara with eigenvalue, then the corresponding eigenvectors satisfyeigenvectors (3) (3) which is equivalent to the homogeneous system (4) (4) The last equation can be written compactly as

Bina Nusantara where is the identity matrix. As shown in Cramer's rule, a linear system of equations has nontrivial solutions iff the determinant vanishes, so the solutions of the last equation are given byidentity matrixCramer's rulelinear system of equationsiffdeterminant This equation is known as the characteristic equation of, and the left-hand side is known as the characteristic polynomial.characteristic equationcharacteristic polynomial For example, for a matrix, the eigenvalues are (7) (7) which arises as the solutions of the characteristic equationcharacteristic equation

Bina Nusantara Kerjakan latihan dalam modul soal