Eigenvalues and singular values

<eig> - Eigenvalues and eigenvectors.

EIG Eigenvalues and eigenvectors.

E = EIG(X) is a vector containing the eigenvalues of a square

matrix X.

[V,D] = EIG(X) produces a diagonal matrix D of eigenvalues and a

full matrix V whose columns are the corresponding eigenvectors so

that X*V = V*D.

[V,D] = EIG(X,'nobalance') performs the computation with balancing

disabled, which sometimes gives more accurate results for certain

problems with unusual scaling. If X is symmetric, EIG(X,'nobalance')

is ignored since X is already balanced.

E = EIG(A,B) is a vector containing the generalized eigenvalues

of square matrices A and B.

[V,D] = EIG(A,B) produces a diagonal matrix D of generalized

eigenvalues and a full matrix V whose columns are the

corresponding eigenvectors so that A*V = B*V*D.

EIG(A,B,'chol') is the same as EIG(A,B) for symmetric A and symmetric

positive definite B. It computes the generalized eigenvalues of A and B

using the Cholesky factorization of B.

EIG(A,B,'qz') ignores the symmetry of A and B and uses the QZ algorithm.

In general, the two algorithms return the same result, however using the

QZ algorithm may be more stable for certain problems.

The flag is ignored when A and B are not symmetric.

See also condeig, eigs, ordeig.

Overloaded methods:

codistributed/eig

sym/eig

Reference page in Help browser

doc eig

<svd> - Singular value decomposition.

SVD Singular value decomposition.

[U,S,V] = SVD(X) produces a diagonal matrix S, of the same

dimension as X and with nonnegative diagonal elements in

decreasing order, and unitary matrices U and V so that

X = U*S*V'.

S = SVD(X) returns a vector containing the singular values.

[U,S,V] = SVD(X,0) produces the "economy size"

decomposition. If X is m-by-n with m > n, then only the

first n columns of U are computed and S is n-by-n.

For m <= n, SVD(X,0) is equivalent to SVD(X).

[U,S,V] = SVD(X,'econ') also produces the "economy size"

decomposition. If X is m-by-n with m >= n, then it is

equivalent to SVD(X,0). For m < n, only the first m columns

of V are computed and S is m-by-m.

See also svds, gsvd.

Overloaded methods:

codistributed/svd

frd/svd

sym/svd

Reference page in Help browser

doc svd

<gsvd> - Generalized singular value decomposition.

GSVD Generalized Singular Value Decomposition.

[U,V,X,C,S] = GSVD(A,B) returns unitary matrices U and V,

a (usually) square matrix X, and nonnegative diagonal matrices

C and S so that

A = U*C*X'

B = V*S*X'

C'*C + S'*S = I

A and B must have the same number of columns, but may have

different numbers of rows. If A is m-by-p and B is n-by-p, then

U is m-by-m, V is n-by-n and X is p-by-q where q = min(m+n,p).

SIGMA = GSVD(A,B) returns the vector of generalized singular