Fr.: matrice adjointe
The → transpose of a → matrix in which each → element is replaced by its → cofactor. Same as → conjugate transpose and → Hermitian conjugate.
Fr.: matrice identité
In linear algebra, the simplest nontrivial diagonal matrix, an n-by-n square matrix with ones on the main diagonal and zeros elsewhere.
Fr.: matrice jacobienne
In → vector calculus, the matrix of all → first-order partial derivatives of a vector-valued → function.
mâtris-e Jordan (#)
Fr.: matrice de Jordan
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.
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.
Fr.: calcul matriciel
The treatment of matrices whose entries are functions.
Fr.: matrice inverse
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.
Fr.: matrice non singulière
A → square matrix that is not a → singular matrix.
Fr.: matrice nulle
An m × n matrix whose elements are all zeros. Also known as zero matrix.
mâtrishâ-ye hamânand (#)
Fr.: matrices similaires
Two → square matrices A and B that are related by B = X-1AX, where X is a square → nonsingular matrix.
Fr.: matrice singulière
A → square matrix that does not have a → matrix inverse.
Fr.: matrice carée
A → matrix with equal numbers of → rows and → columns (i.e., an n × n matrix).
trace of a matrix
Fr.: trace de matrice
Of a → square matrix, the → sum of the entries in the → main diagonal, i.e.: tr(A) = a11 + a22 + ... + ann = Σ aii (i = 1 to n).
Fr.: matrice transposée
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.
mâtris-e yekâyi, ~ yekâni
Fr.: matrice unitaire
A square matrix whose inverse equals its adjoint.
Fr.: matrice nulle
Same as → null matrix.