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Equivalent Conditions for a Matrix to be Invertible
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Classroom Contents
Linear Algebra
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- 1 Linear Equations Introduction
- 2 Solving Systems of Linear Equations
- 3 Using Matrices to Solve Systems of Linear Equations
- 4 Reduced Row Echelon Form
- 5 Gaussian Elimination
- 6 Existence and Uniqueness of Solutions
- 7 Linear Equations Setup
- 8 Matrix Addition and Scalar Multiplication
- 9 Matrix Multiplication
- 10 Properties of Matrix Multiplication
- 11 Interpretations of Matrix Multiplication
- 12 Introduction to Vectors (Math 210)
- 13 Solving Vector Equations
- 14 Solving Matrix Equations
- 15 Matrix Inverses
- 16 Matrix Inverses for 2x2 Matrices
- 17 Equivalent Conditions for a Matrix to be Invertible
- 18 Properties of Matrix Inverses
- 19 Transpose
- 20 Symmetric and Skew-symmetric Matrices
- 21 Trace
- 22 The Determinant of a Matrix
- 23 Determinant and Elementary Row Operations
- 24 Determinant Properties.
- 25 Invertible Matrices and Their Determinants
- 26 Eigenvalues and Eigenvectors
- 27 Properties of Eigenvalues
- 28 Diagonalizing Matrices
- 29 Dot Product (Linear Algebra)
- 30 Unit Vectors
- 31 Orthogonal Vectors
- 32 Orthogonal Matrices
- 33 Symmetric Matrices and Eigenvectors and Eigenvalues
- 34 Symmetric Matrices and Eigenvalues and Eigenvectors - Proofs
- 35 Diagonalizing Symmetric Matrices
- 36 Linearly Independent Vectors
- 37 Gram-Schmidt Orthogonalization
- 38 Singular Value Decomposition - Introduction
- 39 Singular Value Decomposition - How To Find It
- 40 Singular Value Decomposition - Why It Works
