Please help with these additional questions.
(1) The covariant components of a second order tensor with respect to the basis
e=i+i, e=i+i,e=i+i are given by (a[ij]) = array([[2,0,1],[-1,2,0],[0,2,-1]]) Find the components a^ij, a[i]^k, a[k]^i
Can Maple be used to test infinite series for convergence ?
Are the many tests for convergence already built-in Maple ?
Show that Sum(1/((2*n-1)*(2*n+1)), n = 1..infinity) = 1/2)
Hint. (Show by mathematical induction that s[m] = m/(2*m+1)
Can the commutator command in the tensors package be used with tensors of rank greater than 1 ?
I recently tried to prove the jacobi identity using the 2 x 2 Pauli Matrices, that I created as arrays, but kept getting an error message saying something about the improper rank, of the arguments of the commutator command.
I noticed in the help pages that the arguments of commutator must be of rank 1.
I also tried all combinations of covariance and contravariance of the pauli matrices, but nothing worked.
Can anyone help with this ?
Is there any way to get around this ?
The special linear group SL(2)consists of all 2 x 2 matrices (with complex elements) having a determinant of +1. Show that such matrices form a group. Note. The SL(2) group can be related to the full Lorentz group in Section 4.4, much as the SU(2) group is related to SO(3).
Arfken, and Weber.