Definition
Linear Algebra is the branch of mathematics concerning linear equations, linear functions, and their representations in vector spaces and through matrices.
Why It Matters
Linear algebra is the language of high-dimensional data. Any system with multiple variables—from an economy to a neural network—is modeled in vector space, making this the essential toolkit for modern science and technology.
Core Concepts
- Vectors and Vector Spaces: Mathematical objects that can be added together and multiplied by scalars.
- Matrices and Determinants: Rectangular arrays of numbers used to represent linear transformations.
- Linear Transformations: Functions between vector spaces that preserve the operations of vector addition and scalar multiplication.
- Eigenvalues and Eigenvectors: Scalars and vectors that describe the fundamental scaling properties of a linear transformation.