Linear Algebra Definition
A system of linear equations a x b is homogeneous if b 0.
Linear algebra definition. In mathematics linear refers to an equation or function that is the equation of a straight line and takes the form y mx b where m is equal to the slope and b is equal to the y intercept. Home math algebra what does linear mean in mathematics. A linear equation is an algebraic equation such as y 4x 3 in which the variables are of the first degree that is raised only to the first power. This document contains denitions of some of the important terms used in linear algebra. A linear function is any function that graphs to a straight line.
Two systems of linear equations in n unknowns are equivalent if they have the same set of solutions. Linear algebra definition is a branch of mathematics that is concerned with mathematical structures closed under the operations of addition and scalar multiplication and that includes the theory of systems of linear equations matrices determinants vector spaces and linear transformations. Linear algebra is the branch of mathematics concerning linear equations such as. Khan academy is a nonprofit with the mission of providing a free world class education for anyone anywhere. Illustrated definition of linear equation.
Often written in the form. The graph of such an equation is a straight line. Learn for free about math art computer programming economics physics chemistry biology medicine finance history and more. An equation that makes a straight line when it is graphed. An arbitrary subset of a linear space like say a cantor set has nothing to do with linear algebra methods so the definition is made to exclude such things.
All of these denitions should be memorized and not just memorized but understood. Denitions of linear algebra terms in order to learn and understand mathematics it is necessary to understand the meanings of the terms vocabulary words that are used. The motivation for insisting on this is that when we want to do linear algebra we need things to be linear spaces.
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