invertible's Usage Examples:

In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate), if there exists an n-by-n square matrix B such that.

product of two invertible matrices is again invertible, and the inverse of an invertible matrix is invertible, with identity matrix as the identity element.

without violating the rules of counterpoint are said to be in invertible counterpoint.

S} is called invertible in S {\displaystyle S} .

An element with an inverse element only on one side is left invertible or right invertible.

Those that do are called invertible.

GLn(R) of invertible matrices.

For a commutative ring R, an element A of Mn(R) is invertible if and only if the determinant of A is invertible in R.

knot theory, an invertible knot is a knot that can be continuously deformed to itself, but with its orientation reversed.

A non-invertible knot is any knot.

By the LU decomposition algorithm, an invertible matrix may be written as the product of a lower triangular matrix L and.

group GL(n) (a group consisting of all invertible n×n matrices).

In particular, the identity matrix is invertible—with its inverse being precisely itself.

necessarily invertible, which requires that the function is bijective.

In fact, to turn an injective function f : X → Y into a bijective (hence invertible) function.

Every n×n Stieltjes matrix is invertible to a nonsingular symmetric nonnegative matrix, though the converse of.

B = Q − 1 A P {\displaystyle \!B=Q^{-1}AP} for some invertible n-by-n matrix P and some invertible m-by-m matrix Q.

origin is removed from the real line, then the result is the set of 1×1 invertible real matrices, which is homotopy-equivalent to a discrete two-point space.

one of the following concepts: the group under multiplication of the invertible elements of a field, ring, or other structure for which one of its operations.

an invertible matrix used to encrypt the session keys, and the encrypted session keys must be sent along with the ciphertext.

Since only invertible matrices.

chirality can be further classified depending on whether or not it is invertible.

composition of two given morphisms are related to each other by higher order invertible morphisms (2-simplices thought of as "homotopies").

mathematics, the notion of cancellative is a generalization of the notion of invertible.

fundamental results in matrix algebra, that A is invertible if and only if det(A) is an invertible element of R.