I have an equation of the form: $$x'Ax - B$$ where $A$ is a positive definite matrix. I want to solve this equation for $x$. Could anyone provide me with some suggestions on how to solve this kind of quadratic expression?
2026-04-12 18:46:06.1776019566
Solving a quadratic expression
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Making a guess about what you might mean by the word solve. First, find a Cholesky decomposition $$ C^T C = A. $$ Find $$ W = C^{-1}. $$ Take any real column vector $y$ such that $$ |y|^2 = y \cdot y = B. $$ Then $$ x = W y $$ gives $$ x^T A x = B. $$