Videos by the Author of the textbook

Linear Algebra Done Right, 

Videos by Dr. Sheldon Axler

These videos should inform and entertain you, while providing insight and motivation. Click on a link below to see a video about the corresponding section of Linear Algebra Done Right (third edition) [if you are in a country where YouTube is blocked, try this website Links to an external site. instead of the links below].

Each “slides” link gives a pdf file of the slides that accompany the corresponding video. These slides are designed to be viewed in Adobe Acrobat, not a web browser. For a single large pdf file containing the slides (without dropdown features and with less red) for all 50 videos, click here Links to an external site..

• Introduction Links to an external site.
  slides Links to an external site. (save and then open in Adobe Acrobat)

• Section 1.A: Rⁿ and Cⁿ Links to an external site.
  slides Links to an external site. (save and then open in Adobe Acrobat)

• Section 1.B: Definition of Vector Space Links to an external site.
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• Section 1.C: Subspaces Links to an external site.
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• Section 2.A: Span and Linear Independence Links to an external site.
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• Section 2.B: Bases Links to an external site.
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• Section 2.C: Dimension Links to an external site.
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• Section 3.A: The Vector Space of Linear Maps Links to an external site.
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• Section 3.B: Null Spaces and Ranges Links to an external site.
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• Section 3.C: Matrices, part 1: The Matrix of a Linear Map Links to an external site.
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• Section 3.C: Matrices, part 2: Matrix Multiplication Links to an external site.
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• Section 3.D: Invertibility and Isomorphic Vector Spaces Links to an external site.
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• Section 3.E: Products and Quotients of Vector Spaces, part 1: Products Links to an external site.
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• Section 3.E: Products and Quotients of Vector Spaces, part 2: Quotients Links to an external site.
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• Section 3.F: Duality, part 1: Dual Bases and Dual Maps Links to an external site.
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• Section 3.F: Duality, part 2: Annihilators and the Matrix of a Dual Map Links to an external site.
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• Chapter 4: Polynomials Links to an external site.
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• Section 5.A: Invariant Subspaces Links to an external site.
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• Section 5.B: Eigenvectors and Upper-Triangular Matrices, part 1: Existence of Eigenvalues Links to an external site.
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• Section 5.B: Eigenvectors and Upper-Triangular Matrices, part 2: Upper-Triangular Matrices Links to an external site.
  slides Links to an external site. (save and then open in Adobe Acrobat)

• Section 5.C: Eigenspaces and Diagonal Matrices Links to an external site.
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• Section 6.A: Inner Products and Norms, part 1: Inner Products Links to an external site.
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• Section 6.A: Inner Products and Norms, part 2: Norms Links to an external site.
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• Section 6.B: Orthonormal Bases Links to an external site.
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• Section 6.C: Orthogonal Complements and Minimization Problems, part 1: Orthogonal Complements Links to an external site.
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• Section 6.C: Orthogonal Complements and Minimization Problems, part 2: Minimization Problems Links to an external site.
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• Section 7.A: Self-Adjoint and Normal Operators, part 1: Adjoints Links to an external site.
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• Section 7.A: Self-Adjoint and Normal Operators, part 2: Self-Adjoint Operators Links to an external site.
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• Section 7.A: Self-Adjoint and Normal Operators, part 3: Normal Operators Links to an external site.
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• Section 7.B: The Spectral Theorem Links to an external site.
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• Section 7.C: Positive Operators and Isometries, part 1: Positive Operators Links to an external site.
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• Section 7.C: Positive Operators and Isometries, part 2: Isometries Links to an external site.
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• Section 7.D: Polar Decomposition and Singular Value Decomposition, part 1: Polar Decomposition Links to an external site.
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• Section 7.D: Polar Decomposition and Singular Value Decomposition, part 2: Singular Value Decomposition Links to an external site.
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• Section 8.A: Generalized Eigenvectors and Nilpotent Operators, part 1: Null Spaces of Powers of an Operator Links to an external site.
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• Section 8.A: Generalized Eigenvectors and Nilpotent Operators, part 2: Generalized Eigenvectors Links to an external site.
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• Section 8.A: Generalized Eigenvectors and Nilpotent Operators, part 3: Nilpotent Operators Links to an external site.
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• Section 8.B: Decomposition of an Operator, part 1: Decomposition Via Generalized Eigenvectors Links to an external site.
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• Section 8.B: Decomposition of an Operator, part 2: Block Diagonal Matrices Links to an external site.
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• Section 8.B: Decomposition of an Operator, part 3: Square Roots of Operators Links to an external site.
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• Section 8.C: Characteristic and Minimal Polynomials, part 1: The Characteristic Polynomial Links to an external site.
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• Section 8.C: Characteristic and Minimal Polynomials, part 2: The Minimal Polynomial Links to an external site.
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• Section 8.D: Jordan form Links to an external site.
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• Section 9.A: Complexification Links to an external site.
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• Section 9.B: Operators on Real Inner Product Spaces, part 1: Normal Operators Links to an external site.
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• Section 9.B: Operators on Real Inner Product Spaces, part 2: Isometries Links to an external site.
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• Section 10.A: Trace, part 1: Change of Basis Links to an external site.
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• Section 10.A: Trace, part 2: Trace of an Operator and of a Matrix Links to an external site.
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• Section 10.B: Determinant, part 1: Determinant of an Operator and of a Matrix Links to an external site.
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• Section 10.B: Determinant, part 2: Change of Variables in Integration in Rⁿ Links to an external site.
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