Manuals/calci/MATRIXSYMMETRIC

• is any matrix.

Description

• This function shows the symmetric value of the given matrix.
• In , is any matrix.
• A matrix is said to be symmetric if .
• 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 .
• So Symmetric matrix entries are .
• 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

Symmetric Matrix