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Understanding Vector Spaces
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Classroom Contents
Linear Algebra
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- 1 Introduction to Linear Algebra: Systems of Linear Equations
- 2 Understanding Matrices and Matrix Notation
- 3 Manipulating Matrices: Elementary Row Operations and Gauss-Jordan Elimination
- 4 Types of Matrices and Matrix Addition
- 5 Matrix Multiplication and Associated Properties
- 6 Evaluating the Determinant of a Matrix
- 7 The Vector Cross Product
- 8 Inverse Matrices and Their Properties
- 9 Solving Systems Using Cramer's Rule
- 10 Understanding Vector Spaces
- 11 Subspaces and Span
- 12 Linear Independence
- 13 Basis and Dimension
- 14 Change of Basis
- 15 Linear Transformations on Vector Spaces
- 16 Image and Kernel
- 17 Orthogonality and Orthonormality
- 18 The Gram-Schmidt Process
- 19 Finding Eigenvalues and Eigenvectors
- 20 Diagonalization
- 21 Complex, Hermitian, and Unitary Matrices
