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Summation 'Sigma' Notation

By Kardi Teknomo, PhD.

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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 .




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.




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

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This tutorial is copyrighted.

Preferable reference for this tutorial is

Teknomo, Kardi (2015) Summation Tutorial. http://people.revoledu.com/kardi/tutorial/basicmath/sum/

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