Learn in the textbookLinear Algebra, Calculus, and Error
DefinitionLinear algebra (線形代数) is the branch of mathematics that uses vectors and matrices to handle many quantities linked by linear expressions all at once.
ExplanationA linear expression, such as y = 2x + 3, is one built only by adding terms of the form constant times variable and a constant. Solving a system of linear equations in one go, or transforming many coordinates at once as when an image is rotated or enlarged, can be described with the ideas of linear algebra. It also underpins computer graphics and machine learning, which process large volumes of numbers in table form.
AnalogyIt is like a building kit with fixed parts (sets and tables of numbers) and fixed assembly steps (multiplication and addition): the same steps process a large batch of numbers together.
Memory hook"Linear" comes from "line": the graph of a linear expression is a straight line.