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DIVISION
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1994-08-07
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DIVISION:
There are two type of division operators, the `/' and the '\'.
The 1st is called "right-division", and the 2nd is called
"left-division".
Right-Division: For scalars the result is what you would
expect. For matrices, A / B is the same as A * inv(B). But,
what really happens is A / B is implemented like (B' \ A')'
The element-by-element version of right-division, `./' is
simply A[i;j] / B[i;j].
Left-Division: For scalars the result of A \ B is B / A. For
matrices the result is the solution to A*X = B. If B has more
than one column, then the result is an X that contains a
column for every column of B, which are the solutions to
A*x[;i] = B[;i].
When the system of equations is determined (square), then
Gaussian elimination is used. Otherwise, a least-squares
solution is performed. If the system is under-determined, a
minimum-norm solution is obtained. For the least-squares
solutions the LAPACK subroutines DGELSS, and ZGELSS are used.
The element-by-element version, `.\' is simply B[i;j] /
A[i;j].