Welcome to the Linear Algebra Gallery! This page showcases various concepts, examples, and applications of linear algebra. Linear algebra is a branch of mathematics that deals with vectors, matrices, and linear transformations. It has applications in many fields such as physics, engineering, computer science, and economics.
Key Concepts
Vectors: A vector is a mathematical object that has both magnitude and direction. In linear algebra, vectors are often represented as column matrices.
Matrices: A matrix is a rectangular array of numbers. Matrices are used to represent systems of linear equations and perform various operations such as multiplication and inversion.
Determinants: The determinant of a matrix is a scalar value that can be calculated from the elements of the matrix. It is used to determine whether a matrix is invertible and to solve systems of linear equations.
Eigenvalues and Eigenvectors: Eigenvalues and eigenvectors are special values and vectors associated with a linear transformation. They have many applications in fields such as quantum mechanics and vibration analysis.
Applications
Computer Graphics: Linear algebra is used in computer graphics for tasks such as transforming objects, rendering images, and simulating physics.
Machine Learning: Linear algebra is used in machine learning algorithms for tasks such as data representation, feature extraction, and model optimization.
Quantum Mechanics: Linear algebra is used in quantum mechanics to describe the state of a quantum system and to perform calculations.
Resources
For further reading on linear algebra, you can visit the following resources: