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What is the meaning of Sigma Symbol?
Greek Alphabet Sigma has been used widely as a notation for summation
Index is always integer.
LastIndex must be greater or equal to the firstIndex .
Example
If we have a sequence of numbers
then we can put index on the sequence such that
,
,
,
,
,
and
Why do we need to put a sigma symbol?
Using this symbol, you can simplify the notation of addition. Instead of writing all the symbols such as
, you can type them neatly as
. Aside from that, using the sigma notation, you may manipulate the sums algebraically without even need to expand them all the sums. Check later in the summation tricks and properties on this tutorial on how to do such algebra manipulation.
Sometimes I see the sigma symbol is without index, what is the meaning?
When the range of index is clear, the firstIndex and lastIndex can be omitted. You do not need to write from where it begins and until what index it stops if people can already understand without them.
Example:
Matrix
Trace of a matrix is the summation of diagonal element of a matrix
When the index is clear, even the index name can be omitted. You do not need to put any index at all. The notation becomes even neater.
Example
: Vector
Length of vector is a square root of the sum of square of vector component
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See Also:
Kardi Teknomo's Tutorial
This tutorial is copyrighted .
Preferable reference for this tutorial is
Teknomo, Kardi (2015) Summation Tutorial. http://people.revoledu.com/kardi/tutorial/BasicMath/Sum/