I need to get a Diagonalized of a matrix. My given matrix is 4*4 strictly Dominant Diagonal matrix.
something like this:
\begin{array}{l}4&2&1&0\\1&5&2&1\\2&0&6&3\\1&1&0&3\end{array}
it seems the result of Diagonalized of matrix ( if it is possible) would be in form of A= S * D * S_inverse. So now I really need to have the D matrix as all entries are integers not fractional. is there any way or any condition that A as strictly Dominant Diagonal matrix can have D as diagonal matrix with all integers?
I used this website for matrix calculation, it is hard to just try infinite numbers to get finally your desired output.
calculator website
EDITED strictly Dominant Diagonal matrix : a matrix which items on diagonal is strictly greater than absolute sum of all items in that row, means a_ii > Sum ( | a_ij | ) for all j, i != j as you see in my example 4 > 2 +1 + 0 and 5 > 1 + 2 + 1 and so on