To be used in future
 Section A.4: Vector calculus Up Appendix A: Useful Mathematics Section A.6: Relativity-tensor notation 

A.5 Matrix algebra

Use the Einstein summation convention↓ in its naive form: any repeated index is summed over
Product of matrices
If is an matrix, and an matrix their product is an matrix with entries
Transpose
If is an matrix, its transpose↓ is an matrix with entries Also
Hermitean conjugate
If is an matrix, its Hermitean conjugate↓ is an matrix with entries Also
Inner (dot, scalar) product↓↓↓
The inner product of two length (complex) vectors is Reinterpreting a vector as a single column matrix (i.e., an matrix), we see that the inner product is the single entry in the matrix ; we shall often ignore the matrix part and write
Solution to linear equations (Cramer’s rule)↓
The solution to the equation which is of course formally can be written in terms of determinants as (this is called Cramer’s rule) where is the matrix with the th column replaced by the vector .
 Section A.4: Vector calculus Up Appendix A: Useful Mathematics Section A.6: Relativity-tensor notation