LINEAR ALGEBRA


Meaning of LINEAR ALGEBRA in English

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 involved

in two dimensions, a x + b y = 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.

Britannica Concise Encyclopedia.      Краткая энциклопедия Британика.