solve.eigen.Hermitian(a, b, tol=0)
eigen.Hermitian
, representing the symmetric
indefinite decomposition of a real symmetric or complex Hermitian matrix.
b
must equal the
dimension of the matrix underlying
a
.
tol
.
By default,
tol
= 0.
A
is the matrix whose eigenvalue decomposition is represented
by
a
, an object of class
"Matrix"
is returned that is the solution
x
to the system of equations A %*% x = b
If
b
is not supplied, the inverse of
A
is returned.
The minimum least-squares solution or pseudo-inverse are returned if
A
is
rank deficient.
Attributes include a copy of the call to
solve
.
Can be used for matrices that are rank-deficient, i.e., whose rank is less than their minimum dimension.
Golub, G. H., and C. F. Van Loan (1989), Matrix Computations, 2nd edition, Johns Hopkins, Baltimore.
n <- 5 a <- Matrix( rnorm(n*n), nrow = n, ncol = n) a[row(a) > col(a)] <- t(a)[row(a) > col(a)] # construct symmetric matrix class(a) <- Matrix.class(x) b <- rnorm(n) z <- eigen(a) # eigenvalue decomposition a %*% solve(a,b) - b # residual (solve(a) %*% b) - solve(a,b)