Solvability conditions for the matrix equation X T DX + AX + X T B + C = 0
Yu. O. Vorontsov · Computational Mathematics and Mathematical Physics · 2015
Under certain restrictions on the matrix coefficients of the quadratic matrix equation X T DX + AX + X T B + C = 0, solvability conditions for this equation are given, and its relationship with an equation of the form XAX = B is found. Certain specific types of matrix coefficients obeying the above solvability conditions are indicated.