LeviCivita({list}) :
"LeviCivita" implements the Levi Civita symbol. This is generally
useful for tensor calculus. {list} should be a list of integers,
and this function returns 1 if the integers are in successive order,
eg. {1,2,3,...} would return 1. Swapping two elements of this
list would return -1. So, LeviCivita( {2,1,3} ) would evaluate
to -1.
Permutations({list})
Permutations({list}) :
Permutations returns a list with all the premutations of the original
list.
InProduct(a,b)
InProduct(a,b) (or alternatively a . b) :
Calculate the inproduct of two vectors.
CrossProduct(a,b)
CrossProduct(a,b) (or alternatively a X b) :
Calculate the crossproduct of two three-dimensional vectors.
ZeroVector(n)
ZeroVector(n) : ZeroVector returns a list with n zeroes.
BaseVector(row,n)
BaseVector(row,n) : BaseVector returns a vector with item row set to 1, the
other n-1 set to zero.
Identity(n)
Identity(n) : Identity returns a identity matrix of dimension n x n.
IsMatrix(x)
IsMatrix(x) : Predicates checking if the object x is a matrix.
Normalize(v)
Normalize(v) : Return the normalized vector v.
ZeroMatrix(n,m)
ZeroMatrix(n,m) : Returns a matrix with n rows and m columns, all zeros.
Transpose(M)
Transpose(M) : Return the transpose of a matrix M.
Determinant(M)
Determinant(M) : Return the determinant of a matrix M.
DiagonalMatrix(v)
DiagonalMatrix(v) : Return a square matrix with the elements of vector
v on the diagonal of the matrix. All other elements are zero.
Trace(M)
Trace(M) : Return the trace of a matrix M (defined as the sum of the
elements on the diagonal of the matrix).
Inverse(M)
Inverse(M) : Return the inverse of matrix M. The determinant of M should
be non-zero.
CoFactor(M,i,j)
CoFactor(M,i,j) : This function returns the cofactor of a matrix around
the element (i,j). The cofactor is the minor times
(-1)^(i+j)
Minor(M,i,j)
Minor(M,i,j) : This function returns the minor of a matrix around
the element (i,j). The minor is the determinant of the matrix
excluding the ith row and jth column.
SolveMatrix(M,v)
SolveMatrix(M,v) : This function returns the vector x that satisfies
the equation "M x = v". The determinant of M should be non-zero.
CharacteristicEquation(matrix,var)
CharacteristicEquation(matrix,var) :
calculate characteristic equation of "matrix", using
"var". The zeros os this equation are the eigenvalues
of the matrix, Det(matrix-I var);
EigenValues
Standard math library
Calling Sequence:
EigenValues(matrix)
Parameters:
matrix - a square matrix
Description:
EigenValues returns the eigenvalues of a matrix.
The eigenvalues x of a matrix M are the numbers such that
M*v=x*v for some vector.
It first determines the characteristic equation, and then factorizes this
equation, returning the roots of the characteristic equation
det(matrix-x*identity).
EigenVectors(matrix,eigenvalues)
Standard math library
Parameters:
matrix - matrix - a square matrix
eigenvalues - list of eigenvalues as returned by EigenValues
Description:
EigenVectors returns a list of the eigenvectors of a matrix.
It uses the eigenvalues and the matrix to set up n equations with
n unknowns for each eigenvalue, and then calls Solve to determine
the values of each vector.