A linear equation is an equation that is written for two different variables. This equation will be a linear combination of these two variables, and a constant can be present. Surprisingly, when any linear equation is plotted on a graph, it will necessarily produce a straight line - hence the name: Linear equations.
A linear equation can be written in different ways. Any simple equation in x and y can be termed as a linear equation if it follows a certain set of rules. For example, the highest (and the only) degree of both - x and y - variables in the equation should be 1. Other than that, constants (zero degree variables) can be there.
|Complexity Classes||Algorithm Paper Links||Lower Bounds Paper Links|
|Polynomial > 3|
|Cubic||[Gaussian-Jordan Elimination (-150)]
|Quadratic||Conjugate Gradient (1952)|
|logn||Harrow (Quantum) (2009)|