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DifferentialGeometry:-Tools[&MatrixMinus, &MatrixMult, &MatrixPlus, &MatrixWedge]

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

A &MatrixMinus B - subtract two Matrices/Vectors of vectors, differential forms or tensors

A &MatrixMult C - multiply a Matrix/Vector A of vectors, differential forms or tensors by a scalar C or a Matrix/Vector C of scalars

C &MatrixMult A - multiply a Matrix A of vectors, differential forms or tensors by a scalar C or a Matrix/Vector C of scalars

A &MatrixPlus B - add two Matrices/Vectors of vectors, differential forms or tensors

E &MatrixWedge F - calculate the Matrix wedge product of two Matrices/Vectors of differential forms.

Parameters

A, B

-

two Matrices/Vectors of vectors, differential forms or tensors

C

-

a scalar or a Matrix/Vector of scalars

E, F

-

two Matrices/Vectors of differential forms

Description

• 

These commands provide, within the DifferentialGeometry environment, the basic arithmetical operations for Matrices or Vectors of: vectors, differential forms, or tensors.  They are particularly useful for curvature calculations for connections on principle bundles of matrix groups.

• 

These commands are part of the DifferentialGeometry:-Tools package, and so can be used in the form described above only after executing the commands with(DifferentialGeometry) and with(Tools) in that order.

Examples

 

Define a 3-dimensional manifold M with coordinates [x, y, z].

 

Example 1 

Define two column Vectors of 1 forms A, B; a 2x2 matrix C of scalars; a row Vector of 1 forms E and a 2x2 Matrix of 1 forms F.

(1)

(2)

(3)

(4)

(5)

Perform various arithmetic operations with the quantities A, B, C, E, F.

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

See Also

DifferentialGeometry

LinearAlgebra

AlgebraicOperations

evalDG

DGzip

Matrix

Vector

 


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