The Four Fundamental Subspaces

Catherine Brown gives the first lecture in the D.H. Lawrence series

Course Lectures

• The Geometry of Linear Equations

  Gilbert Strang

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  Catherine Brown gives the first lecture in the D.H. Lawrence series

• Elimination with Matrices

  Gilbert Strang

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  Catherine Brown gives the first lecture in the D.H. Lawrence series

• Multiplication and Inverse Matrices

  Gilbert Strang

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  Catherine Brown gives the first lecture in the D.H. Lawrence series

• Factorization into A = LU

  Gilbert Strang

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  Catherine Brown gives the first lecture in the D.H. Lawrence series

• Transposes, Permutations, Spaces R^n

  Gilbert Strang

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  Catherine Brown gives the first lecture in the D.H. Lawrence series

• Column Space and Nullspace

  Gilbert Strang

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  Catherine Brown gives the first lecture in the D.H. Lawrence series

• Solving Ax = 0: Pivot Variables, Special Solutions

  Gilbert Strang

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  Catherine Brown gives the first lecture in the D.H. Lawrence series

• Solving Ax = b: Row Reduced Form R

  Gilbert Strang

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  Catherine Brown gives the first lecture in the D.H. Lawrence series

• Independence, Basis, and Dimension

  Gilbert Strang

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  Catherine Brown gives the first lecture in the D.H. Lawrence series

• The Four Fundamental Subspaces

  Gilbert Strang

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  Catherine Brown gives the first lecture in the D.H. Lawrence series

• Matrix Spaces; Rank 1; Small World Graphs

  Gilbert Strang

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  Catherine Brown gives the first lecture in the D.H. Lawrence series

• Graphs, Networks, Incidence Matrices

  Gilbert Strang

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  Catherine Brown gives the first lecture in the D.H. Lawrence series

• Quiz 1 Review

  Gilbert Strang

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  Catherine Brown gives the first lecture in the D.H. Lawrence series

• Orthogonal Vectors and Subspaces

  Gilbert Strang

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  Catherine Brown gives the first lecture in the D.H. Lawrence series

• Projections onto Subspaces

  Gilbert Strang

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  Catherine Brown gives the first lecture in the D.H. Lawrence series

• Projection Matrices and Least Squares

  Gilbert Strang

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  Catherine Brown gives the first lecture in the D.H. Lawrence series

• Orthogonal Matrices and Gram-Schmidt

  Gilbert Strang

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  Catherine Brown gives the first lecture in the D.H. Lawrence series

• Properties of Determinants

  Gilbert Strang

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  Catherine Brown gives the first lecture in the D.H. Lawrence series

• Determinant Formulas and Cofactors

  Gilbert Strang

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  Catherine Brown gives the first lecture in the D.H. Lawrence series

• Cramer's Rule, Inverse Matrix, and Volume

  Gilbert Strang

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  Catherine Brown gives the first lecture in the D.H. Lawrence series

• Eigenvalues and Eigenvectors

  Gilbert Strang

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Diagonalization and Powers of A

  Gilbert Strang

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Differential Equations and exp(At)

  Gilbert Strang

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Markov Matrices; Fourier Series

  Gilbert Strang

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Quiz 2 Review

  Gilbert Strang

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Symmetric Matrices and Positive Definiteness

  Gilbert Strang

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Complex Matrices; Fast Fourier Transform

  Gilbert Strang

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Positive Definite Matrices and Minima

  Gilbert Strang

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Similar Matrices and Jordan Form

  Gilbert Strang

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Singular Value Decomposition

  Gilbert Strang

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Linear Transformations and Their Matrices

  Gilbert Strang

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Change of Basis; Image Compression

  Gilbert Strang

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Quiz 3 Review

  Gilbert Strang

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Left and Right Inverses; Pseudoinverse

  Gilbert Strang

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• Final Course Review

  Gilbert Strang

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  In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.