Inner Product Spaces
  • Definition of Inner Product
  • Orthogonality
  • Orthonormal Basis
Linear Transformations
  • Basic Properties
  • Kernel and Image of Linear Transformation
  • Matrix of Linear Transformation
Eigenvalues and Eigenvectors & Diagonalization
-Eigenvalues and Eigenvectors
  • Matrices and Matrix Operations
  • Elementary Row Operations
  • Inverse of Matrix
  • Special Matrices
  • Definition of Determinant
  • Properties of Determinants
  • The Adjoint Matrix
Systems of Linear Equations
  • Gauss and Gauss–Jordan Methods
  • Homogeneous systems of linear equations
  • Cramer’s Rule
Vector Spaces
  • Definition of a Vector Space
  • Subspaces
  • Linear Combination and Spanning Sets
  • Linear Dependence & Linear Independence
  • Basis and Dimension
  • Coordinates and Change of Basis
  • Rank of the Matrix
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