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

sigma notation

Index is always integer.

LastIndex must be greater or equal to the firstIndex .


sigma notation

If we have a sequence of numbers sigma notation then we can put index on the sequence such that sigma notation , sigma notation , sigma notation , sigma notation , sigma notation , sigma notation and

sigma notation

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 sigma notation , you can type them neatly as sigma notation . 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.


Matrix sigma notation

Trace of a matrix is the summation of diagonal element of a matrix

sigma notation

sigma notation

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 sigma notation

Length of vector is a square root of the sum of square of vector component

sigma notation

sigma notation

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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.