Linear Algebra

Linear Algebra is the branch of mathematics concerning vector spaces and linear mappings between them. It provides the essential tools for representing and manipulating data, understanding geometric transformations, and solving systems of equations – core operations in machine learning and data analysis.

This section includes:

• Core Objects: Definitions and properties of Scalars, Vectors, Matrices, and Tensors.
• Basic Operations: How to perform fundamental calculations like vector addition, scalar multiplication, dot products, and matrix multiplication.
• Matrix Properties: Key concepts associated with matrices, such as the Identity Matrix, Matrix Inverse, Determinant, and Trace.
• Vector Spaces: Foundational ideas like Linear Independence, Span, Basis, Dimension, and Rank.
• Norms: Methods for measuring the size or length of vectors and matrices, including L1, L2, and Frobenius norms, essential for regularization and distance calculations.
• Decompositions: Techniques for factoring matrices into simpler components, focusing on Eigenvalues and Eigenvectors and the Singular Value Decomposition (SVD).

Use the sidebar navigation to explore specific topics within Linear Algebra.