Nonsingular Matrix


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Related to Nonsingular Matrix: symmetric matrix, Inverse of a matrix

nonsingular matrix

[′nän‚siŋ·gyə·lər ′mā·triks]
(mathematics)
A matrix which has an inverse; equivalently, its determinant is not zero.

Nonsingular Matrix

 

in mathematics, a square matrix A = ǀǀaijǀǀ1n of order n whose determinant \A\ is nonzero. Every nonsingular matrix is invertible. A nonsingular matrix defines a nonsingular linear transformation in n-dimensional space. The passage from one coordinate system to another is also defined by a nonsingular matrix.

References in periodicals archive ?
where V is a nonsingular matrix and C, N are square Jordan blocks corresponding to eigenvalues lying in [C.sup.-] (open left-half complex plane) and [[??].sup.+] (open right-half complex plane), respectively.
Since B is a nonsingular matrix based on the algebraic knowledge one can have [x.sup.*] - [y.sup.*] = 0 or [x.sup.*] = [y.sup.*].
if there exists a nonsingular matrix S (t) with real entries such that
Thus, we can find a nonsingular matrix P consisting of the n independent eigenvectors of A so that
Let us apply a transformation of variable x(k) = Q[??](k) with a nonsingular matrix Q to system (3):
for all t [member of] R, any k [member of] {0, 1, ..., n} and any i [member of] {1, ..., n}, where N is a nonsingular matrix such that [N.sup.-1] AN is a Jordan form matrix and [[[N.sup.-1][[vector].[upsilon]](s)].sub.i] denotes the i-th component of [N.sup.-1][[vector].[upsilon]](s).
It is well known that a nonsingular matrix over any field has a unique inverse.
Let S be the nonsingular matrix that contains these eigenvectors as columns [S.sub.:k], and let [Lambda] = Diag([[Lambda].sub.k]) be the associated diagonal matrix of eigenvalues [[Lambda].sub.k] (k = 1, ..., m).
Let a nonsingular matrix A [member of] [C.sup.n x n] and a vector b [member of] [C.sup.n] be given.
with the nonsingular matrix (<[L.sub.k], [[??].sup.j]>), k, j = [bar.1,n], since (2.5) is valid for every fundamental system and, particulary, for [z.sup.j] = [[??].sup.j], j = [bar.1,n].
It is known that, for every matrix A, there exists a nonsingular matrix S transforming it to the corresponding Jordan matrix form [LAMBDA] = [S.sup.-1] AS.