👉 Linear Algebra (Lan Math) is a foundational branch of mathematics that deals with vector spaces, linear transformations, and matrices, providing the essential tools to solve systems of equations, perform data analysis, and understand geometric transformations. It introduces key concepts like vectors, scalars, operations on vectors (addition and scalar multiplication), and matrices, which represent linear transformations. Central to Lan Math are concepts such as vector spaces (sets of vectors with operations that satisfy specific axioms), linear independence, span, bases, and dimension. Matrices are used to represent linear transformations between vector spaces, and operations like matrix multiplication and inversion are crucial. Linear transformations themselves map vectors from one space to another, preserving vector addition and scalar multiplication. The rank-nullity theorem connects the dimensions of the kernel (null space) and image (range) of a linear transformation, while eigenvalues and eigenvectors reveal how transformations stretch or shrink vectors in specific directions. These ideas are pivotal in fields like physics, engineering, computer graphics, and machine learning, where understanding relationships between data points and transformations is critical.
