Linear Algebra

See https://understandinglinearalgebra.org/home.html

1: Linear Equations §

• Linear Equation
• Linear System
• Consistency
• Matrix Representation Of A Linear System
• Row Echelon Form
• Reduced Row Echelon Form
• Gauss-Jordan Elimination

2: Matrices & Determinants §

• Matrix
• Matrix Operations
  • Matrix Multiplication
  • Matrix Transposition
• Matrix Variants
  • Identity Matrix
• Inverse Matrix
  • Calculating Inverse Matrices
• Rank
• Determinant
  • Calculating Determinant

3: Euclidean Vector Spaces §

• Real Space
  • 3D Real Space
• Vector
  • Vector Basics
  • Vector Operation
  • Vector Projection
  • Dot Product
  • Cross Product
  • Scalar Triple Product
• Vector Line
• Plane

4: General Vector Spaces §

• Binary Operations
• Field
  • Axioms of a Field
  • Examples of a Field
• Vector Space
  • Axioms of a Vector Space
  • Examples of a Vector Space
• Subspace
• Linear Dependence
• Basis
  • Dimension
• Linear Span
• Extracting a Basis from a Spanning Set
• Solution Space
• Column Space & Row Space of a Matrix
• Nullity
• Coordinates Relative to a Basis

5: General Linear Transformations §

• Linear Transformation
• Geometric Transformation
• Kernel
• Image
• Function
• Invertible Linear Transformation
• Change of Basis

6: Eigenvalues, Eigenvectors and Eigenspace §

• Eigenvalue
• Eigenvector
• Obtaining the Eigenvectors from a Matrix
• Eigenspace
• Diagonalisable
• Diagonalising A Matrix

7: Inner Product Spaces §

• Inner Product
• Complex Dot Product
• Geometry from Inner Products
• Orthogonality
• Gram-Schmidt
• Least Squared Error Fitting
• Orthogonal Matrix
• Using Orthogonal Matrices

Short description

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• 3D Real Space
• Axioms of a Field
• Axioms of a Vector Space
• Basis
• Binary Operations
• Calculating Inverse Matrices
• Calculating Determinant
• Change of Basis
• Column Space & Row Space of a Matrix
• Complex Dot Product
• Consistency
• Converting a General Basis to an Orthonormal Basis
• Coordinates Relative to a Basis
• Cross Product
• Diagonalisable
• Determinant
• Diagonalising A Matrix
• Dimension
• Dot Product
• Eigenvalue
• Eigenspace
• Eigenvector
• Examples of a Vector Space
• Examples of a Field
• Extracting a Basis from a Spanning Set
• Field
• Function - Maths
• Gauss-Jordan Elimination
• Geometric Transformation
• Geometry from Inner Products
• Identity Matrix
• Image - Maths
• Inner Product
• Inverse Matrix
• Invertible Linear Transformation
• Kernel
• Least Squared Error Fitting
• Linear Equation
• Linear Dependence
• Linear Span
• Linear System
• Linear Transformation
• Matrix Multiplication
• Matrix Operations
• Matrix Representation Of A Linear System
• Matrix
• Matrix Transposition
• Matrix Variants
• Nullity
• Obtaining the Eigenvectors from a Matrix
• Orthogonal Matrix
• Orthogonality
• Plane
• Rank
• Real Space
• Reduced Row Echelon Form
• Row Echelon Form
• Scalar Triple Product
• Solution Space
• Subspace
• Support Vector Machines
• Vector Basics
• Vector Line
• Vector Projection
• Vector Space
• Vector
• Elementary Matrix

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