Calendar · Lecture Notes
MIT OpenCourseWare
Linear Algebra
Art: Johannes Kepler, Konjukce Saturnu a Jupiteru Originál, 1596 · Public domain
- Instructor
- David Vogan
- Term
- Fall 2013
- Level
- Undergraduate
- What's inside
- 9 problem sets · 1 reading · 9 other files · 4 web pages
- Materials open
- MIT OCW
About this course
Source: MIT OpenCourseWare 18.700 Linear Algebra, Fall 2013, David Vogan — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.
Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.
Before you start
Prerequisites are not listed here. Check MIT's own syllabus for this course.
How this course was organized
What's here, and what isn't
- MIT's own materials here did not support a verified, course-wide order, so they are grouped by section instead.
Not included here
1 item from the source could not be safely included:
- MIT's page format for this item wasn't recognized clearly enough to place it safely.
Materials by section
Grouped by section, as MIT organized them. Not sequenced or ordered.
Assignments
10 files
- Old Assignments 9 Download
- 18.700 Fall 2013 Problem Set 1 Download
- 18.700 Fall 2013 Problem Set 2 Download
- 18.700 Fall 2013 Problem Set 3 Download
- 18.700 Fall 2013 Problem Set 4 Download
- 18.700 Fall 2013 Problem Set 5 Download
- 18.700 Fall 2013 Problem Set 6 Download
- 18.700 Fall 2013 Problem Set 7 Download
- 18.700 Fall 2013 Problem Set 8 Download
- 18.700 Fall 2013 Problem Set 9 Download
Study Materials
Course outline
Calendar · Lecture Notes
Lecture 2: Subspaces, sums and direct sums
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Lecture 3: Span, independence, bases
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Lecture 4: Bases and dimension
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Lecture 5: Linear maps, null space / range
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Lecture 6: matrices, invertibility
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Lecture 7: Exam 1 on Chapters 1–3
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Lecture 8: Finite fields. Systems of equations.
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Lecture 9: Gaussian elimination
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Lecture 10: Counting over Fp. Invariant subspaces.
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Lecture 11: Finding eigenvectors
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Lecture 12: Upper triangular and diagonal matrices
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Lecture 13: Eigen vectors over R and Fp
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Lecture 14: Exam 2 on Chapters 1–5
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Lecture 15: Inner products, Gram-Schmidt
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Lecture 16: Orthogonal projection, minimization
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Lecture 17: Adjoint, self-adjoint, normal
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Lecture 18: Spectral theorem
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Lecture 19: Positive operators
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Lecture 20: Isometries, polar decomposition
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Lecture 21: Exam 3 on Chapters 1–7
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Lecture 22: Generalized eigenspaces
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Lecture 23: Generalized eigenspace decomposition
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Lecture 24: Characteristic polynomial
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Lecture 25: Determinant
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Lecture 26: Trace, canonical commutation relations
MIT OpenCourseWare, David Vogan, 18.700 Linear Algebra, Fall 2013.
License: CC BY-NC-SA 4.0 · Edition: Fall 2013 · Open the original course on OCW ↗
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