An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

The → transpose of a → matrix in which each → element is replaced by its → cofactor. Same as → conjugate transpose and → Hermitian conjugate.

→ adjoint; → matrix.

In linear algebra, the simplest nontrivial diagonal matrix, an n-by-n square matrix with ones on the main diagonal and zeros elsewhere.

→ identity; → matrix.

In → vector calculus, the matrix of all → first-order partial derivatives of a vector-valued → function.

→ Jacobian; → matrix.

A square matrix with a constant value λ (nonzero) along the diagonal, 1's on the superdiagonal, and all other elements 0.

Named after Marie Ennemond Camille Jordan (1838-1922), French mathematician who pioneered group theory, wrote on the theory of linear differential equations, and on the theory of functions, which he applied to the curve which bears his name. → matrix.

1) An orderly array of numbers, algebraic symbols, or mathematical functions, especially when such arrays are added and multiplied according to certain rule; e.g. → Jordan matrix.
2) The fine grained material found in between the → chondrules, fragments and metal grains found inside → stony meteorites.

From O.Fr. matrice, from L. matrix "female animal kept for breeding," in L.L. "womb, source, origin," from mater, → mother.

Mâtris, loan from Fr., as above.

The treatment of matrices whose entries are functions.

→ matrix; → calculus.

For a → square matrix whose → determinant is not zero, the unique matrix A^-1 satisfying the relation AA^-1 = A^-1A = I, where I is the → identity matrix.

→ matrix; → inverse.

A → square matrix that is not a → singular matrix.

→ non-; → singular; → matrix.

An m × n matrix whose elements are all zeros. Also known as zero matrix.

→ null; → matrix.

Two → square matrices A and B that are related by B = X^-1AX, where X is a square → nonsingular matrix.

→ similar; → matrix.

A → square matrix that does not have a → matrix inverse.

→ singular; → matrix.

A → matrix with equal numbers of → rows and → columns (i.e., an n × n matrix).

→ square; → matrix.

Of a → square matrix, the → sum of the entries in the → main diagonal, i.e.: tr(A) = a₁₁ + a₂₂ + ... + a_nn = Σ a_ii (i = 1 to n).

→ trace; → matrix.

The matrix of → order n x m obtained from a matrix of order m x n by exchanging the order of the → rows and → columns.

Tansposed, p.p. of → transpose; → matrix.

A square matrix whose inverse equals its adjoint.

→ unitary; → matrix.

Same as → null matrix.

→ zero; → matrix.