Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Problem

At 12:25 PM 9/19/01 -0400, I wrote:
As for notation, the appropriate combination of standard symbols
appears adequate to the task.

Let me be a little more specific. Suppose we have two vectors V and A:

1) We can calculate the component of A in the direction of V using the
following projection operator
Pij = Vi Vj / V dot V
whenever V has a direction at all, i.e. whenever |V| is nonzero.
B := parallel component of A
Bi = Pij Aj

2) We can calculate the component of A transverse to V using the
projection operator (1-Pij).
C := transverse component of A
Ci = (1-Pij) Aj