Question

Is there a solution for AX=B matrix equation with zero diagonal constraint, such that: X_ii=0 ?
where, A, B, X are n×n matrices.

Is it right to solve the equation as follows?

X=inv(A)*B
X_ii=0

Answer 1

Answer on Question #67456 – Math – Linear Algebra

Question

Is there a solution for $AX = B$ matrix equation with zero diagonal constraint, such that: $X_{ii} = 0$?

Is it right to solve the equation as follows?

$$X = A^{-1}B$$ $$X_{ii} = 0$$

Solution

Solving the equation $AX = B$:

$$A^{-1}AX = A^{-1}B$$ $$EX = A^{-1}B$$ $$X = A^{-1}B$$

where $E$ is identity matrix.

The diagonal values of $X$ are already determined by $A^{-1}B$ and cannot be separately constrained.

It is possible to have $X_{ii} = 0$ if the diagonal of $A^{-1}B$ consists of zeros.

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