R: Positive Definiteness of a Matrix, Rank and Condition Number
rank.condition
R Documentation
Positive Definiteness of a Matrix, Rank and Condition Number
Description
is.positive.definite tests whether all eigenvalues of a symmetric matrix
are positive.
make.positive.definite computes the nearest positive definite of a
real symmetric matrix, using the algorithm of NJ Higham (1988, Linear Algebra
Appl. 103:103-118).
rank.condition estimates the rank and the condition
of a matrix by
computing its singular values D[i] (using svd).
The rank of the matrix is the number of singular values D[i] > tol)
and the condition is the ratio of the largest and the smallest
singular value.
The definition tol= max(dim(m))*max(D)*.Machine$double.eps
is exactly compatible with the conventions used in "Octave" or "Matlab".
Also note that it is not checked whether the input matrix m is real and symmetric.
tolerance for singular values and for absolute eigenvalues
- only those with values larger than
tol are considered non-zero (default:
tol = max(dim(m))*max(D)*.Machine$double.eps)
method
Determines the method to check for positive definiteness:
eigenvalue computation (eigen, default) or Cholesky decomposition
(chol).
Value
is.positive.definite returns
a logical value (TRUE or FALSE).
rank.condition returns a list object with the following components:
rank
Rank of the matrix.
condition
Condition number.
tol
Tolerance.
make.positive.definite returns a symmetric positive definite matrix.