Manuals/calci/DIAGONALMATRIX

MATRIX (TypeOfMatrix,DimensionsOfMatrix,SeedValuesToUse,IJFunction,PreParameter,IsItInternalCall)

• $TypeOfMatrix$ is the type of the matrix.
• $DimensionsOfMatrix$ is the order of the diagonal matrix.

Description

• This function shows the Diagonal matrix of a given order.
• In $MATRIX(TypeOfMatrix,DimensionsOfMatrix,SeedValuesToUse,IJFunction,PreParameter,IsItInternalCall$, $DimensionsOfMatrix$ is the order of square matrix.
• A diagonal matrix is a square matrix which is of the form $a_{ij}=c_{i}\delta _{ij}$ where $\delta _{ij}$ is the Kronecker delta, $c_{i}$ are constants, and i,j=1, 2, ..., n.
• The general diagonal matrix is of the form:

${\begin{bmatrix}c_{1}&0&\cdots &0\\0&c_{2}&\cdots &0\\\vdots &\vdots &\ddots &\vdots \\0&0&\cdots &c_{n}\end{bmatrix}}$

• So the main diagonal entries are need not to be zero and off-diagonal entries are zero.
• That is,the matrix D = (di,j) with n columns and n rows is diagonal if:

$\forall i,j\in {1,2,....n},i\neq j\Rightarrow d_{i,j}=0$

See Also

• DIAGONALFILL
• ARROWHEAD
• MATRIXOPERATORS

References

• Diagonal matrix

• List of Main Z Functions

• Z3 home