Branch of algebra concerned with methods of solving systems of linear equations; more generally, the mathematics of linear transformations and vector spaces. Linear refers to the form of the equations involvedin two dimensions, ax + by = c. Geometrically, this represents a line. If the variables are replaced by vectors, functions, or derivatives, the equation becomes a linear transformation. A system of equations of this type is a system of linear transformations. Because it shows when such a system has a solution and how to find it, linear algebra is essential to the theory of mathematical analysis and differential equations. Its applications extend beyond the physical sciences into, for example, biology and economics.
This entry comes from Encyclopædia Britannica Concise.
For the full entry on linear algebra, visit Britannica.com.
Seen & Heard
What made you look up linear algebra? Please tell us what you were reading, watching or discussing that led you here.