Study guides, Class notes & Summaries
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Lecture 8: Rank-Nullity Theorem and Coordinates
- Class notes • 3 pages • 2023
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Linear Algebra with Applications (Fifth Edition) by Otto Bretsch 
3.3 The Dimension of a Subspace of R^n 
3.4 Coordinates
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Lecture 9: Change of Basis Matrix
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Linear Algebra with Applications (Fifth Edition) by Otto Bretsch 
3.3 The Dimension of a Subspace of R^n 
3.4 Coordinates
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Lecture 10: Orthogonality
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Linear Algebra with Applications (Fifth Edition) by Otto Bretsch 
5.1 Orthogonal Projections and Orthonormal Bases
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Lecture 11: Finding Orthonormal Bases
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Linear Algebra with Applications (Fifth Edition) by Otto Bretsch 
5.1 Orthogonal Projections and Orthonormal Bases 
5.2 Gram-Schmidt Process and QR Factorization
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Lecture 12: Orthogonal Matrices
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Linear Algebra with Applications (Fifth Edition) by Otto Bretsch 
5.3 Orthogonal Transformations and Orthogonal Matrices 
5.4 Least Squares and Data Fitting
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Lecture 13: Determinants
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Linear Algebra with Applications (Fifth Edition) by Otto Bretsch 
6.1 Introduction to Determinants
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Lecture 14: Properties of the Determinant
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Linear Algebra with Applications (Fifth Edition) by Otto Bretsch 
6.2 Properties of the Determinant
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Lecture 15: Eigenvalues and Eigenvectors
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Linear Algebra with Applications (Fifth Edition) by Otto Bretsch 
7.1 Diagonalization
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Lecture 16: Finding Eigenvalues and Eigenvectors
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Linear Algebra with Applications (Fifth Edition) by Otto Bretsch 
7.2 Finding the Eigenvalues of a Matrix 
7.3 Finding the Eigenvectors of a Matrix
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Lecture 17: More About Eigenvalues/Eigenvectors
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Linear Algebra with Applications (Fifth Edition) by Otto Bretsch 
7.4 More on Dynamical Systems 
7.5 Complex Eigenvalues
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