 First edition cover | |
| Author | Jack L. Chalker |
|---|---|
| Country | United States |
| Language | English |
| Genre | Science fiction |
| Publisher | Timescape Books |
Publication date | July, 1982 |
| Media type | Print (Paperback) |
| ISBN | 0-671-44481-6 |
The Identity Matrix is a science fiction novel by American writer Jack L. Chalker, published in 1982 by Timescape Books. The work focuses on the body swap and enemy mine plot devices, as well as a background conflict between two powerful alien races. [1]
In linear algebra, the determinant is a scalar value that can be computed from the elements of a square matrix and encodes certain properties of the linear transformation described by the matrix. The determinant of a matrix A is denoted det(A), det A, or |A|. Geometrically, it can be viewed as the volume scaling factor of the linear transformation described by the matrix. This is also the signed volume of the n-dimensional parallelepiped spanned by the column or row vectors of the matrix. The determinant is positive or negative according to whether the linear mapping preserves or reverses the orientation of n-space.
In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument. That is, for f being identity, the equality f(x) = x holds for all x.
In linear algebra, the trace of a square matrix A is defined to be the sum of elements on the main diagonal of A.
In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere. It is denoted by In, or simply by I if the size is immaterial or can be trivially determined by the context. Less frequently, some mathematics books use U or E to represent the identity matrix, meaning "unit matrix" and the German word Einheitsmatrix respectively.
In linear algebra, an orthogonal matrix is a square matrix whose columns and rows are orthogonal unit vectors.
In mathematics, the general linear group of degree n is the set of n×n invertible matrices, together with the operation of ordinary matrix multiplication. This forms a group, because the product of two invertible matrices is again invertible, and the inverse of an invertible matrix is invertible, with identity matrix as the identity element of the group. The group is so named because the columns of an invertible matrix are linearly independent, hence the vectors/points they define are in general linear position, and matrices in the general linear group take points in general linear position to points in general linear position.
In mathematics, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The result matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix.
In mathematics, a square matrix is a matrix with the same number of rows and columns. An n-by-n matrix is known as a square matrix of order . Any two square matrices of the same order can be added and multiplied.
In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. An example of a 2-by-2 diagonal matrix is , while an example of a 3-by-3 diagonal matrix is. An identity matrix of any size, or any multiple of it, is a diagonal matrix.
In linear algebra, an n-by-n square matrix A is called invertible if there exists an n-by-n square matrix B such that
In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots. It has the determinant and the trace of the matrix as coefficients. The characteristic polynomial of an endomorphism of vector spaces of finite dimension is the characteristic polynomial of the matrix of the endomorphism over any base; it does not depend on the choice of a basis. The characteristic equation is the equation obtained by equating to zero the characteristic polynomial.
In mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column and 0s elsewhere. Each such matrix, say P, represents a permutation of m elements and, when used to multiply another matrix, say A, results in permuting the rows or columns of the matrix A.
In mathematics, the Woodbury matrix identity, named after Max A. Woodbury says that the inverse of a rank-k correction of some matrix can be computed by doing a rank-k correction to the inverse of the original matrix. Alternative names for this formula are the matrix inversion lemma, Sherman–Morrison–Woodbury formula or just Woodbury formula. However, the identity appeared in several papers before the Woodbury report.
In mathematics, particularly linear algebra, a zero matrix or null matrix is a matrix all of whose entries are zero. It also serves as the additive identity of the additive group of matrices, and is denoted by the symbol or —followed by subscripts corresponding to the dimension of the matrix as the context sees fit. Some examples of zero matrices are
In mathematics, a zero element is one of several generalizations of the number zero to other algebraic structures. These alternate meanings may or may not reduce to the same thing, depending on the context.
In linear algebra, an augmented matrix is a matrix obtained by appending the columns of two given matrices, usually for the purpose of performing the same elementary row operations on each of the given matrices.
In mathematics, an elementary matrix is a matrix which differs from the identity matrix by one single elementary row operation. The elementary matrices generate the general linear group of invertible matrices. Left multiplication (pre-multiplication) by an elementary matrix represents elementary row operations, while right multiplication (post-multiplication) represents elementary column operations.
In mathematics, an involutory matrix is a matrix that is its own inverse. That is, multiplication by matrix A is an involution if and only if A2 = I. Involutory matrices are all square roots of the identity matrix. This is simply a consequence of the fact that any nonsingular matrix multiplied by its inverse is the identity.
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. For example, the dimension of the matrix below is 2 × 3, because there are two rows and three columns:
Lesbian, gay, bisexual, and transgender (LGBT) persons in Lesotho face legal challenges not experienced by non-LGBT residents. Lesotho does not recognise same-sex marriages or civil unions, nor does it ban discrimination on the basis of sexual orientation or gender identity.