Manuals/calci/DIAGONALWITH

DIAGONALWITH(Matrix,Properties,Seed,Offset,FillTypeAntiColumnOrRow)

• $Matrix$ is any nxn square matrix.

Description

• This function gives the matrix satisfying the diagonal properties.
• An diagonal matrix is a matrix where all the entries are zero on the main diagonal going from the upper left corner to the lower right corner ($\nearrow$).
• In Diagonalwith, all the elements on main diagonal are filled with the given Properties rather than by 0.
• 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.