# Manuals/calci/SYMMETRIC

MATRIX("SYMMETRIC",order)

• 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 ,where denotes the transpose.
• i.e., A square matrix which is equal to its transpose is called symmetric matrix.
• So .
• This also implies , 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

• 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.

## Examples

• 1.MATRIX("symmetric") =84
• 2.MATRIX("symmetric",3)
 -10 88 92 88 14 -21 92 -21 -29
• 3.MATRIX("symmetric:boolean",4)
 1 0 1 1 0 0 1 0 1 1 0 1 1 0 1 1
• 4.MATRIX("symmetric:integer",5)
 -76 -15 7 -100 -28 -15 -32 -98 -100 -87 7 -98 47 52 -72 -100 -100 52 -63 8 -28 -87 -72 8 76

## Related Videos

Symmetric Matrices