In Fortran a vector or matrix start with \( 1 \), but it is easy
to change a vector so that it starts with zero or even a negative number.
If we have a double precision Fortran vector which starts at \( -10 \) and ends at \( 10 \), we could declare it as
REAL(KIND=8) :: vector(-10:10). Similarly, if we want to start at zero and end at 10 we could write
REAL(KIND=8) :: vector(0:10).
We have also seen that Fortran allows us to write a matrix addition \( \mathbf{A} = \mathbf{B}+\mathbf{C} \) as
A = B + C. This means that we have overloaded the addition operator so that it translates this operation into
two loops and an addition of two matrix elements \( a_{ij} = b_{ij}+c_{ij} \).