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Linear Algebra Wiki
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The Complex Numbers
The Complex Numbers
The Complex Numbers
Exercises
Solutions
Systems of Linear Equations
Systems of Linear Equations
Linear Equations
Linear Systems
Elementary Operations
Matrices
Gaussian Elimination
Exercises
Solutions
Vector Spaces
Vector Spaces
R², R³ and Rⁿ
Solution Sets of Homogeneous Systems
Intersections of Subspaces
Further Examples
Linear Combinations
Linear Independence
Bases
Dimension
Exercises
Solutions
Linear Maps
Linear Maps
Definition and First Examples
Matrix-Vector Multiplication
Kernel and Image (1)
Kernel and Image (2)
Revisiting Linear Systems
Linear Maps on Basis Vectors
Matrices of Linear Maps
Composing Linear Maps
Inverses
Change of Basis
Transposition
Exercises
Solutions
Determinants
Determinants
2×2 Determinants
Determinants of Larger Matrices
Invertibility and Determinants
Further Properties
Exercises
Solutions
Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors
Definitions
Characteristic Polynomial
Eigenspaces
Diagonalization
Exercises
Solutions
Euclidean Spaces
Euclidean Spaces
Scalar Product on Rⁿ
Euclidean Spaces
Orthogonal and Symmetric Matrices
Affine Subspaces
Distances
Summary
Exercises
Solutions
Appendix
Appendix
Mathematical Notation
Interactive Visualizations
Linear Algebra Wiki
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Welcome to the companion wiki for the Linear Algebra lecture.