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• The Concept of an Eigenvector, 3.

• Right Eigenvector Matrix.

• Eigenvector amplitudes.

• Eigenvalue and Eigenvector.

• Traversing the potential energy surface by eigenvector-following: applications to global optimisation and the structural transformations of clusters.
• Steps are directly taken between minima using eigenvector-following. ...

• Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | Viewers | New papers by email | Author registration | Rankings | Volunteers | FAQ | Help! Individual Tracking of an Eigenvalue and Eigenvector of a Parameterized Matrix.

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• The scalar is then called the eigenvalue associated with the eigenvector. ...
• (Complex eigenvalue, eigenvector pairs exist). ...
• then we say that v is an eigenvector of the operator A, and its associated eigenvalue is c. Note that if v is an eigenvector with eigenvalue c , then any non-zero multiple of v is also an eigenvector with eigenvalue c. ...
• and therefore 2 is an eigenvalue of A and we have found a corresponding eigenvector. ...
• An important tool for describing eigenvalues of square matrices is the characteristic polynomial: saying that c is an eigenvalue of A is equivalent to stating that the system of linear equations ( A - c I) x = 0 (where I is the identity matrix) has a non-zero solution x (namely an eigenvector), and so it is equivalent to the determinant det( A - c I) being zero. ...
• For example, take the bilateral shift on the Hilbert space ; it is easy to see that any potential eigenvector can't be square-summable, so none exist. ...
• MathWorld: Eigenvector .
• Earliest Known Uses of Some of the Words of Mathematics: E - see eigenvector and related terms .
• Vectors | Vector spaces | Linear span | Linear transformation | Linear independence | Linear combination | Basis | Column space | Row space | Dual space | Orthogonality | Eigenvector | Eigenvalue | Least squares regressions | Outer product | Cross product | Dot product | Transpose | Matrix decomposition .
• ) It uses material from the Wikipedia article "Eigenvector". ...
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• Re: Very simple eigenvector/eigenvalue calculation   7. ...
• Very simple eigenvector/eigenvalue calculation 7. ...
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• Voice recognition using an eigenvector.
• Each of the library voices has a predetermined eigenvector and an inner product frequency distribution of inner products between the eigenvector and the frames of its voice pattern. Then, inner products between the voice pattern of the input voice signal and the eigenvector of each of the candidate library voice are calculated. ...
• (1) an eigenvector having a non-zero minimum eigenvalue; and.
• (2) an inner product frequency distribution of inner products between (i) the frames of each of said candidate voice patterns and (ii) said eigenvector;.
• (c) calculating an inner product frequency distribution of inner products between the frames of said input voice pattern and the eigenvector of each of said plurality of candidate voice patterns; and.
• This invention generally relates to a method and system for recognizing an unknown voice by comparing it with a plurality of known voices, and, in particular, to a method and system for recognizing an unknown input voice utilizing an eigenvector obtained by the principal component analysis method.
• In accordance with the present invention, there is provided a method for recognizing an input voice in which a time-spectral pattern having time information and a plurality of frames is obtained from the input voice and the time-spectral pattern is subjected to the principal component analysis method to determine a non-zero eigenvector which is then applied to the time-spectral pattern to determine the distribution of inner products between the eigenvector and the frames of the time-spectral pattern.
• 2 is subjected to the well-known principal component analysis to determine a non-zero minimum eigenvector, which is an eigenvector having a non-zero, minimum eigenvalue and, then, inner products between the thus obtained eigenvector and the frames of the voice pattern of FIG. ...
• An eigenvector R for one word voice is defined by the following expression. It is to be noted that such an eigenvector can be determined for a voice pattern of the format shown in FIG. ...
• Here, ##EQU1## And, an inner product between the eigenvector R and Xi can be defined by the following expression. ... This operation is carried out for each of the known voices to define a histogram of inner products obtained as inner products between the eigenvector R and the frames of a voice pattern. ...
• DETERMINATION OF EIGENVECTOR R.
• It is important to determine an eigenvector such that the spread of the distribution of values of inner products is limited so as to limit the memory capacity required to store the inner product frequency distribution. In the first place, an eigenvector is determined so as to minimize the scatter or variance of the inner products (R, Xi). ... Then, among the eigenvalues thus determined, a non-zero and smallest eigenvalue is selected and its corresponding eigenvector is determined for the particular voice pattern. ... Then, a histogram of inner products is determined and stored in the library 5 together with its eigenvector.

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