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<div style="font-size:30px">'''SYMMETRIC'''</div><br/>
<div style="font-size:30px">'''MATRIX("SYMMETRIC",order)'''</div><br/>
*<math>order</math> is the size of the Symmetric matrix.
==Description==
*This function returns the symmetric matrix of order 3.
*A symmetric matrix is a square matrix that satisfies <math>A^(T)=A</math>,where <math>A^(T)</math> denotes the transpose.
*i.e., A square matrix which is equal to its transpose is called symmetric matrix.
*So <math>a_(ij)=a_(ji)</math>.
*This also implies <math>A^(-1)A^(T)=I</math>, where I is the identity matrix.
*Because equal matrices have equal dimensions, only square matrices can be symmetric.
*An example for the symmetric matrix is
<math>A=\begin{pmatrix}
43 & -5 & -93 \\
-5 & -11 & -75 \\
-93 & -75 & -7 \\
\end{pmatrix}
*The properties of symmetric matrices are:
*1.Every square diagonal matrix is symmetric, since all off-diagonal entries are zero.
*2.Similarly, each diagonal element of a skew-symmetric matrix must be zero, since each is its own negative.
*3.Hermitian matrices are a useful generalization of symmetric matrices for complex matrices.
*In Calci, MATRIX("symmetric") gives the symmetric matrix with the integer numbers.
*The other way to give the syntax is MATRIX("symmetric:integer).The syntax is to get the positive numbers symmetric matrix is MATRIX("symmetric:positive integer").
*To get a negative numbers symmetric matrix is MATRIX("symmetric:negative integer").
*Also to get the symmetric matrix with the elements 0 and 1(boolean numbers) users give syntax as MATRIX("symmetric:boolean").
*So using Calci users can get a different types of symmetric matrices.