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DifferentialGeometry:-Tools[&MatrixMinus, &MatrixMult, &MatrixPlus, &MatrixWedge]
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.
Perform various arithmetic operations with the quantities A, B, C, E, F.
See Also
DifferentialGeometry, LinearAlgebra, AlgebraicOperations, evalDG, DGzip, Matrix, Vector
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