Manuals/calci/MATRIXSYMMETRIC

MATRIXSYMMETRIC (GeneratedMatrix,About)

• $GeneratedMatrix$ is any matrix.

Description

• This function shows the symmetric value of the given matrix.
• In $MATRIXSYMMETRIC(GeneratedMatrix,About)$,$GeneratedMatrix$ is any matrix.
• A matrix is said to be symmetric if $A=A^{T}$.
• $A^{T}$ is the transpose of the matrix A.
• Normally equal matrices have equal dimensions, only square matrices can be symmetric.
• But using this function we can get the symmetric matrix even non square matrix also.
• Consider the matrix $A=(a_{ij})$.
• So Symmetric matrix entries are $(a_{ij})=a_{ji}$.
• 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.

Examples

1. MATRIXSYMMETRIC([12,16,20;98,76,56;34,54,28])

12	98	20
98	76	56
20	56	28

2. MATRIXSYMMETRIC([[2,17,18,-34,98],[60,3.15,36,23,13],[54,55,3,19,25],[65,45,77,-90,88.8]])

2	60	54	-34	98
60	3.15	55	23	13
54	55	3	19	25
-34	23	19	-90	88.8

See Also

• MATRIXMULTIPLY
• MATRIXOPERATORS
• MATRIXMOD

References

• Symmetric

• List of Main Z Functions
• Z3 home