Linear Algebra
A number of linear algebra-related functions.
Matrices
Produce clock matrix [WikClock]. |
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Produce the CNOT matrix [WikCNOT]. |
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Generate the Fourier transform matrix [WikDFT]. |
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Produce a Gell-Mann operator [WikGM]. |
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Produce a generalized Gell-Mann operator [WikGM2]. |
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Produce generalized Pauli operator [WikGenPaul]. |
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Produce a |
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Calculate the |
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Produce a Pauli operator [WikPauli]. |
Produce a |
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Create standard basis of dimension dim. |
Operations on Matrices and Vectors
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Compute the Kronecker tensor product [WikTensor]. |
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Perform the unvec operation on a vector to obtain a matrix [Rigetti2020]. |
Perform the vec operation on a matrix [WATVEC]. |
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Compute the inner product \(\langle v_1|v_2\rangle\) of two vectors [WikInner]. |
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Compute the outer product \(|v_1\rangle\langle v_2|\) of two vectors. |
Properties of Matrices and Vectors
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Check if matrix is block positive [1]_. |
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Determine if two linear operators commute with each other [WikCom]. |
Check if matrix is a density matrix [WikDensity]. |
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Determine if a matrix is diagonal [WikDiag]. |
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Check if matrix is Hermitian [WikHerm]. |
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Check if matrix is the identity matrix [WikIdentity]. |
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Check if matrix is the idempotent matrix [WikIdempotent]. |
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Determine if a matrix is normal [WikNormal]. |
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Check if the vectors are orthonormal. |
Determine if a matrix is a permutation matrix [WikiPermutation]. |
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Check if matrix is positive definite (PD) [WikPD]. |
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Check if matrix is a projection matrix [WikProj]. |
Check if matrix is positive semidefinite (PSD) [WikPSD]. |
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Determine if a matrix is square [WikSquare]. |
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Determine if a matrix is symmetric [WikSym]. |
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Check if matrix is unitary [WikUnitary]. |
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Determine if one vector or matrix majorizes another. |
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Compute the S(k)-norm of a matrix [1]_. |