Results 301 to 310 of about 36,403 (314)
Some of the next articles are maybe not open access.
1992
Unless otherwise noted, we will assume throughout this chapter that all vector spaces are finite dimensional.
openaire +2 more sources
Unless otherwise noted, we will assume throughout this chapter that all vector spaces are finite dimensional.
openaire +2 more sources
2012
The physical relevance and importance of eigenvalues and eigenvectors. The power method and the QR method for calculating all or individual eigenvalues and eigenvectors of a given matrix.
C. Phillips, C. Woodford
openaire +4 more sources
The physical relevance and importance of eigenvalues and eigenvectors. The power method and the QR method for calculating all or individual eigenvalues and eigenvectors of a given matrix.
C. Phillips, C. Woodford
openaire +4 more sources
1993
This chapter introduces and, to a limited extent, solves one of the classical problems associated with linear processes: their decomposition into well-behaved, independent component subprocesses. What is especially noteworthy and exciting about the material is that it uses all of the major concepts introduced so far, including the representation of ...
openaire +2 more sources
This chapter introduces and, to a limited extent, solves one of the classical problems associated with linear processes: their decomposition into well-behaved, independent component subprocesses. What is especially noteworthy and exciting about the material is that it uses all of the major concepts introduced so far, including the representation of ...
openaire +2 more sources
1997
The eigenvectors of H n can be constructed in many ways. One method is to use a modal matrix. Following Yarlagadda and Hershey (1982a) we first define a modal matrix. T n , of H n by $${T_n} = {H_n} + {\Lambda_n} $$ (14) where Λn is a diagonal matrix of the eigenvalues of H n as suggested by Kremer (1973) who continued on to suggest Gram ...
R. K. Rao Yarlagadda, John Erik Hershey
openaire +2 more sources
The eigenvectors of H n can be constructed in many ways. One method is to use a modal matrix. Following Yarlagadda and Hershey (1982a) we first define a modal matrix. T n , of H n by $${T_n} = {H_n} + {\Lambda_n} $$ (14) where Λn is a diagonal matrix of the eigenvalues of H n as suggested by Kremer (1973) who continued on to suggest Gram ...
R. K. Rao Yarlagadda, John Erik Hershey
openaire +2 more sources
1996
As mentioned in the previous chapter, besides the significance of matrix simplification through elimination, it is often important to simplify a matrix by preserving its eigenvalues. Eigenvalues and their associated eigenvectors are useful in a variety of situations.
Anastasios A. Tsonis, James B. Elsner
openaire +2 more sources
As mentioned in the previous chapter, besides the significance of matrix simplification through elimination, it is often important to simplify a matrix by preserving its eigenvalues. Eigenvalues and their associated eigenvectors are useful in a variety of situations.
Anastasios A. Tsonis, James B. Elsner
openaire +2 more sources
1996
Let a ∈ and a ≠0. Prove that the eigenvectors of the matrix $$ \left( {\begin{array}{*{20}c} 1 & a \\ 0 & 1 \\ \end{array} } \right) $$ generate a 1-dimensional space, and give a basis for this space.
openaire +2 more sources
Let a ∈ and a ≠0. Prove that the eigenvectors of the matrix $$ \left( {\begin{array}{*{20}c} 1 & a \\ 0 & 1 \\ \end{array} } \right) $$ generate a 1-dimensional space, and give a basis for this space.
openaire +2 more sources
1971
Publisher Summary This chapter explores a particular invariant property of some mappings. Eigen is a German word meaning special, and an eigenvector of a mapping is a special vector whose direction is invariant under, or reversed by, the mapping. The chapter discusses the mappings of the x–y-plane and of x–y–z-space.
openaire +2 more sources
Publisher Summary This chapter explores a particular invariant property of some mappings. Eigen is a German word meaning special, and an eigenvector of a mapping is a special vector whose direction is invariant under, or reversed by, the mapping. The chapter discusses the mappings of the x–y-plane and of x–y–z-space.
openaire +2 more sources
Approximation of Eigenvalues and Eigenvectors
2006In this chapter we deal with approximations of the eigenvalues and eigen-vectors of a matrix A ∈ ℂn×n Two main classes of numerical methods exist to this purpose, partial methods, which compute the extremal eigen-values of A (that is, those having maximum and minimum module), or global methods, which approximate the whole spectrum of A.
Alfio Quarteroni +2 more
openaire +2 more sources
2017
Suppose we measure the height and weight of a collection of people. We could make a plot of the results, using an asterisk for each person. The horizontal position is determined by the person’s height, and the vertical position is determined by the person’s weight. The resulting plot might look something like that shown in Figure 11-1.
openaire +2 more sources
Suppose we measure the height and weight of a collection of people. We could make a plot of the results, using an asterisk for each person. The horizontal position is determined by the person’s height, and the vertical position is determined by the person’s weight. The resulting plot might look something like that shown in Figure 11-1.
openaire +2 more sources