| Метод |
Описание |
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dataProviderForInverse ( ) |
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dataProviderForInverseProductIsReverseProductOfInverses ( ) |
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dataProviderForKroneckerProductDeterminant ( ) |
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dataProviderForMatrixTimesIdentityIsOriginalMatrix ( ) |
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dataProviderForMultiplicationIsAssociative ( ) |
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dataProviderForMultiplicationIsDistributive ( ) |
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dataProviderForOneSquareMatrix ( ) |
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dataProviderForScalarMultiplicationOrder ( ) |
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dataProviderForScalarMultiplicationOrderAddition ( ) |
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dataProviderForSolve ( ) |
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dataProviderForSymmetric ( ) |
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dataProviderForThreeMatrices ( ) |
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dataProviderForTwoSquareMatrices ( ) |
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testDeterminantProductSameAsProductOfDeterminants ( array $A, array $B ) |
det(AB) = det(A)det(B)
Determinant of product of matrices is the same as the product of determinants. |
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testDeterminantSameAsDeterminantOfTranspose ( array $A ) |
det(A) = det(Aᵀ)
Determinant of matrix is the same as determinant of transpose. |
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testInverseOfInverseIsOriginalMatrix ( array $A ) |
Axiom: (A⁻¹)⁻¹ = A
Inverse of inverse is the original matrix. |
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testInverseProductIsReverseProductOfInverses ( array $A, array $B ) |
(AB)⁻¹ = B⁻¹A⁻¹
The inverse of a product is the reverse product of the inverses. |
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testInverseWithLUDecompositionInverse ( array $A ) |
(PA)⁻¹ = (LU)⁻¹ = U⁻¹L⁻¹
Inverse of the LU decomposition equation is the inverse of the other side. |
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testKroneckerProductAssociativity ( array $A, array $B, array $C ) |
Axiom: (A ⊗ B) ⊗ C = A ⊗ (B ⊗ C)
Kronecker product associative |
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testKroneckerProductBilinearity1 ( array $A, array $B, array $C ) |
Axiom: A ⊗ (B + C) = A ⊗ B + A ⊗ C
Kronecker product bilinearity |
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testKroneckerProductBilinearity2 ( array $A, array $B, array $C ) |
Axiom: (A + B) ⊗ C = A ⊗ C + B ⊗ C
Kronecker product bilinearity |
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testKroneckerProductDeterminant ( array $A, array $B ) |
Axiom: det(A ⊗ B) = det(A)ᵐ det(B)ⁿ
Determinant of Kronecker product - where A is nxn matrix, and b is nxn matrix |
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testKroneckerProductInverse ( array $A, array $B ) |
Axiom: (A ⊗ B)⁻¹ = A⁻¹ ⊗ B⁻¹
Inverse of Kronecker product |
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testKroneckerProductScalarMultiplication ( array $A, array $B ) |
Axiom: (kA) ⊗ B = A ⊗ (kB) = k(A ⊗ B)
Kronecker product scalar multiplication |
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testKroneckerProductTranspose ( array $A, array $B ) |
Axiom: (A ⊗ B)ᵀ = Aᵀ ⊗ Bᵀ
Transpose of Kronecker product |
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testLUDecompositionAEqualsPInverseLU ( array $A ) |
A = P⁻¹LU |
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testLUDecompositionPAEqualsLU ( array $A ) |
PA = LU
Basic LU decomposition property that permutation matrix times the matrix is the product of the lower and upper decomposition matrices. |
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testLUDecompositionPPTransposeEqualsIdentity ( array $A ) |
PPᵀ = I = PᵀP
Permutation matrix of the LU decomposition times the transpose of the permutation matrix is the identity matrix. |
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testMatrixTimesIdentityIsOriginalMatrix ( array $A ) |
Axiom: AI = A = IA
Matrix multiplied with the identity matrix is the original matrix. |
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testMatrixTimesInverseIsIdentity ( array $A, array $A⁻¹ ) |
Axiom: AA⁻¹ = I = A⁻¹A
Matrix multiplied with its inverse is the identity matrix. |
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testMultiplicationIsAssociative ( array $A, array $B, array $C ) |
Axiom: (AB)C = A(BC)
Matrix multiplication is associative |
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testMultiplicationIsDistributive ( array $A, array $B, array $C ) |
Axiom: A(B + C) = AB + AC
Matrix multiplication is distributive |
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testPInverseEqualsPTranspose ( array $A ) |
P⁻¹ = Pᵀ
Inverse of the permutation matrix equals the transpose of the permutation matrix |
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testScalarMultiplcationOrder ( array $A, array $B, integer $r ) |
Axiom: r(AB) = (rA)B = A(rB)
Order of scalar multiplication does not matter. |
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testScalarMultiplicationOfTransposeOrder ( array $A ) |
(rA)ᵀ = rAᵀ
Scalar multiplication order does not matter for transpose |
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testScalarMultiplicationOrderAddition ( array $A, array $B, integer $r ) |
Axiom: r(A + B) = rA + rB
Order of scalar multiplication does not matter. |
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testSolveEquationForZero ( array $A, array $b, array $x, array $zeros ) |
Axiom: Ax - b = 0
Matrix multiplied with unknown x vector subtract solution b is 0 |
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testSolveInverseBEqualsX ( array $A, array $b, array $x, array $zeros ) |
Axiom: x = A⁻¹b
Matrix multiplied with unknown x vector subtract solution b is 0 |
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testSymmetricEqualsTranspose ( array $A ) |
Axiom: A = Aᵀ
Symmetric matrix is the same as its transpose |
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testSymmetricInverseTranposeEqualsIdentity ( array $A ) |
Axiom: A⁻¹Aᵀ = I
Symmetric matrix inverse times tranpose equals identity matrix |
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testTraceIsSameAsTraceOfTranspose ( array $A ) |
tr(A) = tr(Aᵀ)
Trace is the same as the trace of the transpose |
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testTraceOfProductIsSameRegardlessOfOrderMultiplied ( array $A, array $B ) |
tr(AB) = tr(BA)
Trace of product does not matter the order they were multiplied |
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testTransposeOfInverseIsInverseOfTranspose ( array $A ) |
(A⁻¹)ᵀ = (Aᵀ)⁻¹
The transpose of the inverse is the inverse of the transpose. |
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testTransposeOfTransposeIsOriginalMatrix ( array $A ) |
(Aᵀ)ᵀ = A
The transpose of the transpose is the original matrix. |
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testTransposeProductIsProductOfTranposesInReverseOrder ( array $A, array $B ) |
(AB)ᵀ = BᵀAᵀ
Transpose of a product of matrices equals the product of their transposes in reverse order. |
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testTransposeSumIsSameAsSumOfTransposes ( array $A, array $B ) |
(A + B)ᵀ = Aᵀ + Bᵀ
Transpose of sum is the same as sum of transposes |
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