Linear Algebra
Definition
Linear algebra is a branch of mathematics that deals with vector spaces and linear transformations. It involves studying systems of linear equations, matrices, and their properties.
Analogy
Think of linear algebra as the language of lines and planes in space. Just like how we use words to communicate ideas, linear algebra allows us to express mathematical concepts related to lines and planes.
Related terms
Matrices: Matrices are rectangular arrays of numbers or symbols arranged in rows and columns. They are used to represent systems of linear equations and perform operations such as addition, subtraction, multiplication, and finding inverses.
Vector Space: A vector space is a set of vectors that satisfy certain properties such as closure under addition and scalar multiplication. It provides a framework for studying vectors and their operations in a systematic way.
Linear Transformation: A linear transformation is a function that preserves vector addition and scalar multiplication. It maps vectors from one vector space to another while maintaining linearity properties such as preserving parallelism and the origin.
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