Further Properties of Matrices

A few hints on how to manipulate indices in matrix elements. It is most important to recognize that any index that is summed over is a dummy index. The result is independent of what we call it. Thus, 

Second, it is advisable to use different indices when a product of summations 

This becomes mandatory if we reexpress it as a double summation 

Multiplication of a matrix A by a constant c is equivalent to multiplying each aij by c. Two matrices of the same dimension can be added element by element. By combination of these two operations, the matrix elements of C = A i A -h A 2 B are given by c/y = k aij + k2bij. 

A diagonal matrix has only nonvanishing elements along the main diagonal, for example 

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