and unique up to re-ordering. The Schmidt decomposition is essentially a restatement of the singular value decomposition in a different context. Fix orthonormal...

Iwasawa decomposition. The application of the Gram–Schmidt process to the column vectors of a full column rank matrix yields the QR decomposition (it is...

To understand why, one can look at the Schmidt decomposition of a state, which uses singular value decomposition to express a state with limited entanglement...

m\times n} ⁠ matrix. It is related to the polar decomposition. Specifically, the singular value decomposition of an m × n {\displaystyle m\times n} complex...

In linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of...

Shmidta Schmidt reaction Schmidt number Schmidt decomposition, a decomposition of vectors of tensor product spaces Schmidt sting pain index, a scalar...

Erhard Schmidt (13 January 1876 – 6 December 1959) was a Baltic German mathematician whose work significantly influenced the direction of mathematics...

A\mathbf {x} =\mathbf {b} } , the matrix A can be decomposed via the LU decomposition. The LU decomposition factorizes a matrix into a lower triangular matrix...

existence of a non-trivial decomposition, but merely that any such two decompositions (if they exist) are the same. A Remak decomposition, introduced by Robert...

reduced states, since they are of the same value (can be proved from Schmidt decomposition of the state with respect to the bipartition); the result is independent...

It is used to decide the separability of mixed states, where the Schmidt decomposition does not apply. The theorem was discovered in 1996 by Asher Peres...

Hamiltonian, including long-range interactions. The basis of DMET is the Schmidt decomposition for quantum states, which shows that a given quantum many-body state...

algebra problems: QR decomposition (see Householder transformation and Gram–Schmidt decomposition); Singular value decomposition Reduction to Hessenberg...

decomposition. Decomposition can be a gradual process for organisms that have extended periods of dormancy. One can differentiate abiotic decomposition from biotic...

orthogonal matrix and an upper triangular matrix (QR decomposition, a consequence of Gram–Schmidt orthogonalization). It is named after Kenkichi Iwasawa...

special ear decomposition named chain decomposition by one path-generating rule. Schmidt (2013b) shows that non-separating ear decompositions may also be...

Lyapunov-Schmidt decomposition may be used to produce two systems to which the Implicit Function Theorem applies. The Lyapunov-Schmidt decomposition uses...

|\psi \rangle _{AB}\in H_{A}\otimes H_{B}} can be written (using Schmidt decomposition) as | ψ ⟩ A B = ∑ j λ j | j ⟩ A | j ⟩ B {\textstyle |\psi \rangle...

transform these states into each other using the properties of the Schmidt decomposition, effectively defeating the binding property. One subtle assumption...

the purifying system. Nielsen, Michael A.; Chuang, Isaac L., "The Schmidt decomposition and purifications", Quantum Computation and Quantum Information...

as only rarely multipartite pure states admit the generalized Schmidt decomposition | Ψ A 1 … A m ⟩ = ∑ i = 1 min { d A 1 , … , d A m } a i | e A 1...

quantum state | ψ ⟩ A B {\displaystyle |\psi \rangle _{AB}} , using Schmidt decomposition, we see that the reduced density matrices of systems A and B, ρ...

only if their partial states are not pure. To see this, write the Schmidt decomposition of | ψ ⟩ {\displaystyle |\psi \rangle } as | ψ ⟩ = ∑ k = 1 r ψ p...

In a 2000 paper titled "Generalized Schmidt Decomposition and Classification of Three-Quantum-Bit States" Acín et al. described a way of separating out...

an entangled state | ψ ⟩ {\displaystyle |\psi \rangle } have a Schmidt decomposition: | ψ ⟩ = ∑ x p ( x ) | x A ⟩ | x B ⟩ {\displaystyle |\psi \rangle...

\downarrow \downarrow \rangle } These states are written in the form of Schmidt decomposition and in a descending order. We compare the sum of the coefficients...

group theory, is known as the Krull–Schmidt theorem. A special case of a decomposition of a module is a decomposition of a ring: for example, a ring is...

Jordan–Chevalley decomposition of an element in algebraic group as a product of semisimple and unipotent elements The Bruhat decomposition G = B W B {\displaystyle...

involving the separation of covalent bonds in organic matter by thermal decomposition within an inert environment without oxygen. The word pyrolysis is coined...

Humphry Davy would go on to create Decomposition Tables from his preliminary experiments on Electrolysis. The Decomposition Tables would give insight on the...