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With Linearalgebra: 0 D D D 0 A A D D

The document provides information about linear algebra operations and functions including: 1. It lists over 100 linear algebra operations and functions such as Add, Adjoint, BackwardSubstitute, Basis, BezoutMatrix, BilinearForm, CharacteristicMatrix, and more. 2. It provides an example of calculating the determinant of a 6x6 matrix using the Determinant function and operations like MatrixAdd, MatrixScalarMultiply, and more. 3. The example collects the terms of the determinant calculation with respect to the variable d, resulting in a long polynomial expression involving d.

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Paulo Cavalcante
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60 views2 pages

With Linearalgebra: 0 D D D 0 A A D D

The document provides information about linear algebra operations and functions including: 1. It lists over 100 linear algebra operations and functions such as Add, Adjoint, BackwardSubstitute, Basis, BezoutMatrix, BilinearForm, CharacteristicMatrix, and more. 2. It provides an example of calculating the determinant of a 6x6 matrix using the Determinant function and operations like MatrixAdd, MatrixScalarMultiply, and more. 3. The example collects the terms of the determinant calculation with respect to the variable d, resulting in a long polynomial expression involving d.

Uploaded by

Paulo Cavalcante
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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with LinearAlgebra &x, Add, Adjoint, BackwardSubstitute, BandMatrix, Basis, BezoutMatrix, BidiagonalForm, BilinearForm, CharacteristicMatrix, CharacteristicPolynomial, Column, ColumnDimension,

ColumnOperation, ColumnSpace, CompanionMatrix, ConditionNumber, ConstantMatrix, ConstantVector, Copy, CreatePermutation, CrossProduct, DeleteColumn, DeleteRow, Determinant, Diagonal, DiagonalMatrix, Dimension, Dimensions, DotProduct, EigenConditionNumbers, Eigenvalues, Eigenvectors, Equal, ForwardSubstitute, FrobeniusForm, GaussianElimination, GenerateEquations, GenerateMatrix, Generic, GetResultDataType, GetResultShape, GivensRotationMatrix, GramSchmidt, HankelMatrix, HermiteForm, HermitianTranspose, HessenbergForm, HilbertMatrix, HouseholderMatrix, IdentityMatrix, IntersectionBasis, IsDefinite, IsOrthogonal, IsSimilar, IsUnitary, JordanBlockMatrix, JordanForm, KroneckerProduct, LA_Main, LUDecomposition, LeastSquares, LinearSolve, LyapunovSolve, Map, Map2, MatrixAdd, MatrixExponential, MatrixFunction, MatrixInverse, MatrixMatrixMultiply, MatrixNorm, MatrixPower, MatrixScalarMultiply, MatrixVectorMultiply, MinimalPolynomial, Minor, Modular, Multiply, NoUserValue, Norm, Normalize, NullSpace, OuterProductMatrix, Permanent, Pivot, PopovForm, QRDecomposition, RandomMatrix, RandomVector, Rank, RationalCanonicalForm, ReducedRowEchelonForm, Row, RowDimension, RowOperation, RowSpace, ScalarMatrix, ScalarMultiply, ScalarVector, SchurForm, SingularValues, SmithForm, StronglyConnectedBlocks, SubMatrix, SubVector, SumBasis, SylvesterMatrix, SylvesterSolve, ToeplitzMatrix, Trace, Transpose, TridiagonalForm, UnitVector, VandermondeMatrix, VectorAdd, VectorAngle, VectorMatrixMultiply, VectorNorm, VectorScalarMultiply, ZeroMatrix, ZeroVector, Zip

(1)

0 Md D2$d2 C R1 As$d

D1$d C R1 0

D2$d C S1 As$d

D1$d2 C S1 D3$d2 C S2 K As 0 D2 d2 C R1 As d D1 d2 C R1 0 D2 d2 C S1 As d (2)

D1 d2 C S1 D3 d2 C S2 K As

Determinant M 6 4 2 4 2 2 6 4 4 D2 2 d D1 C D2 d D1 S1 C D2 d S1 C D2 d S1 K D2 d D1 D3 K D2 d D1 S2 C D2 d D1 As K D2 d4 R1 D3 K D2 d2 R1 S2 C D2 d2 R1 As C R1 D1 d4 D2 C R1 D1 d2 S1 C R1 S1 D2 d2 C R1 S2 1
2 2 2 2 4 2 2 K R1 D1 d4 D3 K R1 D1 d2 S2 C R1 D1 d2 As K R2 1 D3 d K R1 S2 C R1 As C As d D1 C As d R1

(3)

collect w.r.t. d

= 2 2 D1 D2 K D1 D2 D3 d6 C R1 D1 D2 K R1 D2 D3 C D1 D2 S1 K R1 D1 D3 C D2 S1 K D1 D2 S2 C D1 D2 As C D1 As d C D2 S1 K R1 D3 C R1 D2 As K R1 D1 S2 C R1 D1 S1 K R1 D2 S2 C R1
2 2 2 2 A2 s C R1 D2 S1 C R1 D1 As d C R1 S1 K R1 S2 C R1 As 2 4 2 2

(4)

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