An Etymological Dictionary of Astronomy and Astrophysics
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فرهنگ ریشه شناختی اخترشناسی-اخترفیزیک

M. Heydari-Malayeri    -    Paris Observatory

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Number of Results: 16 Search : matri
adjoint matrix
  ماتریس ِ آبن   
mârtis-e âban

Fr.: matrice adjointe   

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

adjoint; → matrix.

identity matrix
  ماتریس ِ ایدانی   
mâtris-e idâni

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.

identity; → matrix.

Jacobian matrix
  ماتریس ِ یاکوبی   
mâtris-e Jacobi

Fr.: matrice jacobienne   

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

Jacobian; → matrix.

Jordan matrix
  ماتریس ِ ژوردان   
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.

matrix
  ماتریس   
mâtris (#)

Fr.: matrice   

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.

matrix calculus
  افماریک ِ ماتریس‌ها   
afmârik-e mâtrishâ

Fr.: calcul matriciel   

The treatment of matrices whose entries are functions.

matrix; → calculus.

matrix inverse
  ماتریس ِ وارون   
mâtris-e vârun

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.

matrix; → inverse.

nonsingular matrix
  ماتریس ِ ناتکین   
mâtris-e nâtakin

Fr.: matrice non singulière   

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

non-; → singular; → matrix.

null matrix
  ماتریس ِ نول   
mâtris-e nul

Fr.: matrice nulle   

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

null; → matrix.

similar matrices
  ماتریس‌های ِ همانند   
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.

similar; → matrix.

singular matrix
  ماتریس ِ تکین   
mâtris-e takin

Fr.: matrice singulière   

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

singular; → matrix.

square matrix
  ماتریس ِ چاروش   
matris-e câruš

Fr.: matrice carée   

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

square; → matrix.

trace of a matrix
  مله‌ی ِ ماتریس   
male-ye mâtris

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).

trace; → matrix.

transposed matrix
  ماتریس ِ ترانهاده   
mâtris-e tarânahâdé

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.

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

unitary matrix
  ماتریس ِ یکایی، ~ یکانی   
mâtris-e yekâyi, ~ yekâni

Fr.: matrice unitaire   

A square matrix whose inverse equals its adjoint.

unitary; → matrix.

zero matrix
  ماتریس ِ صفر   
mâtris-e zefr

Fr.: matrice nulle   

Same as → null matrix.

zero; → matrix.