Transcription of Chapter 10 Eigenvalues and Singular Values - MathWorks
{{id}} {{{paragraph}}}
Chapter 10 Eigenvalues and SingularValuesThis Chapter is about Eigenvalues and Singular Values of matrices. Computationalalgorithms and sensitivity to perturbations are both Eigenvalue and Singular Value DecompositionsAneigenvalueandeigenvector of a square matrixAare a scalar and a nonzerovectorxso thatAx= valueand pair ofsingular vectorsof a square or rectangular matrixAare a nonnegative scalar and two nonzero vectorsuandvso thatAv= u,AHu= superscript onAHstands forHermitian transposeand denotes the complexconjugate transpose of a complex matrix. If the matrix is real, thenATdenotes thesame matrix. InMatlab, these transposed matrices are denoted byA'.The term eigenvalue is a partial translation of the German eigenwert. Acomplete translation would be something like own value or characteristic value, but these are rarely used.
The term “eigenvalue” is a partial translation of the German “eigenwert.” A ... The eigenvalue decomposition is an attempt to find a similarity transformation to diagonal form. 10.1. Eigenvalue and Singular Value Decompositions 3 Written in matrix form, the defining equations for singular values and vectors ...
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document:
{{id}} {{{paragraph}}}