French translation for "polar decomposition"

décomposition polaire

Example Sentences:

	1.	Linear algebra calls QS the polar decomposition of M, with S the positive square root of S2 = MTM. QS s'appelle la décomposition polaire de M, où S est la racine carrée positive de S2 = MtM.
	2.	Sylvester called the singular values the canonical multipliers of the matrix A. The fourth mathematician to discover the singular value decomposition independently is Autonne in 1915, who arrived at it via the polar decomposition. Sylvester donna aux valeurs singulières le nom de « multiplicateurs canoniques » d'une matrice A. Le quatrième mathématicien à l'origine de la découverte de cette décomposition est Autonne, en 1915.
	3.	S 2 = ( Q T M ) T ( Q T M ) = M T Q Q T M = M T M {\displaystyle S^{2}=\left(Q^{\mathrm {T} }M\right)^{\mathrm {T} }\left(Q^{\mathrm {T} }M\right)=M^{\mathrm {T} }QQ^{\mathrm {T} }M=M^{\mathrm {T} }M} When M is non-singular, the Q and S factors of the polar decomposition are uniquely determined. S 2 = ( Q t M ) t ( Q t M ) = M t Q Q t M = M t M
	4.	As for matrices, the singular-value factorization is equivalent to the polar decomposition for operators: we can simply write M = U V ∗ ⋅ V T f V ∗ {\displaystyle \mathbf {M} =\mathbf {U} \mathbf {V} ^{*}\cdot \mathbf {V} T_{f}\mathbf {V} ^{*}} and notice that U V* is still a partial isometry while VTf V* is positive. Puisque, pour les matrices, la décomposition en valeurs singulières est équivalente à la décomposition polaire pour les opérateurs, on peut réécrire cela sous la forme : M = U V ∗ ⋅ V T f V ∗

Similar Words：

"polar cap" French translation, "polar circle" French translation, "polar climate" French translation, "polar code (coding theory)" French translation, "polar coordinate system" French translation, "polar desert" French translation, "polar effect" French translation, "polar electro" French translation, "polar exploration" French translation