Foundation subjectLAEN

Linear Algebra

3 topics10 conceptsSource mml-book Used in DBIS MSI Open in graph ↗

Linear algebra used across courses: matrices, rank, invertibility, decompositions.

Generated viewTopics and conceptsshown below

Topics

concepts in learning order

How the determinant measures volume change and singularity, and how it leads through the characteristic polynomial to eigenvalues and eigenvectors, the directions a matrix only scales.

2Inner Products and Norms1 concept

How the dot product induces lengths, distances and angles in $R^n$, and how the angle gives the length-independent cosine similarity used to compare vectors.

Cosine Similarity

3Rank and Invertibility5 concepts

How the rank of a matrix decides whether it is invertible and how many solutions a linear system Ax = b has.

Concept index A–Z

10 concepts · aliases in grey

Characteristic Polynomial → Eigenvalue Charakteristisches Polynom → Eigenvalue cos-similarity → Cosine Similarity Cosine Similaritydet → Determinant Determinant Determinante → DeterminantEigenbasis → Eigenvector Eigenraum → Eigenvector Eigenspace → Eigenvector Eigenspectrum → Eigenvalue Eigenvalue Eigenvalues → Eigenvalue Eigenvector Eigenvectors → Eigenvector Eigenvektor → Eigenvector Eigenwert → EigenvalueHomomorphismus → Linear MapInverse Matrix → Invertible Matrix Invertible Matrix Invertierbare Matrix → Invertible MatrixLGS → System of Linear Equations Linear Equation System → System of Linear Equations Linear Function → Linear Map Linear Map Linear System → System of Linear Equations Linear Transformation → Linear Map Lineare Abbildung → Linear Map Lineares Gleichungssystem → System of Linear Equations Low-Rank Approximation → Singular Value DecompositionMatrix RankNonsingular Matrix → Invertible MatrixPositiv definite Matrix → Positive Semidefinite Matrix Positiv semidefinite Matrix → Positive Semidefinite Matrix Positive Definite Matrix → Positive Semidefinite Matrix Positive Semi-Definite Matrix → Positive Semidefinite Matrix Positive Semidefinite Matrix Positive Semidefiniteness → Positive Semidefinite Matrix PSD Matrix → Positive Semidefinite MatrixRang → Matrix Rank Rang einer Matrix → Matrix Rank Rank → Matrix Rank Rank-k Approximation → Singular Value Decomposition Reduced SVD → Singular Value Decomposition Regular Matrix → Invertible Matrix Reguläre Matrix → Invertible MatrixSingular Matrix → Invertible Matrix Singular Value Decomposition Singular Values → Singular Value Decomposition Singulärwertzerlegung → Singular Value Decomposition Spectrum → Eigenvalue SVD → Singular Value Decomposition System of Linear EquationsTruncated SVD → Singular Value Decomposition