Andrei Antonenko

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Linear Algebra

This is a set of lecture notes and problems I created for Introduction to Linear Algebra taught in Spring 2003 at Applied Mathematics and Statistics Department at Stony Brook University. There are many typos, as I have never fully proof-read them. Please let me know if you find them useful

Lecture Notes

Lecture 01Introduction. Numbers. Sets.
Lecture 02Linear Equations.
Lecture 03Linear Systems. Row Echelon Form. Gaussian Elimination.
Lecture 04Overview of Linear Systems.
Lecture 05Matrices and Matrix Operations.
Lecture 06Inverse and Transpose. Matrices and Linear Systems.
Lecture 07Matrix Equations and the Inverse.
Lecture 08Vector Spaces and Subspaces.
Lecture 09Linear Combinations. Linear Dependence.
Lecture 10Spanning Sets. Basis.
Lecture 11Examples of Bases. Dimension.
Lecture 12More Examples. Dimension and Basis of the Span.
Lecture 13Dimensions and Basis of the Span. Rank.
Lecture 14Functions. Linear Functions.
Lecture 15Homogeneous Systems.
Lecture 16Image and Kernel. Matrix of a Linear Function.
Lecture 17Dimension and Basis of Image and Kernel.
Lecture 18Image and Kernel and Matrices. Linear Functions as a Space.
Lecture 19Area of a Parallelogram.
Lecture 20Permutations.
Lecture 21General Properties of Area and Volume. Determinant.
Lecture 22Properties of Determinants – 1.
Lecture 23Properties of Determinants – 2.
Lecture 23 – Addendum
Proofs.
Lecture 24Application of Determinants. Kramer’s Rule. Inverse.
Lecture 25Euclidean Spaces. Norm. Cauchy Inequality.
Lecture 26Orthogonality.
Lecture 27Orthogonal Bases. Gram-Schmidt Process.
Lecture 28Operators. Change of Basis. Matrix of an Operator.
Lecture 29Change of Matrix of an Operator. Diagonalizable Operators.
Lecture 30Eigenvalues and Eigenvectors.
Lecture 31Symmetric Matrices.
Lecture 32Powers and Square Roots of Matrices.
Lecture 33Invariant Spaces. Jordan Canonical Form.
Lecture 34Functions of Operators

Problem Sets

Problem Set 1Linear Systems.
Problem Set 2Matrices.
Problem Set 3Vector Spaces. Bases and Dimensions.
Problem Set 4Linear Functions.
Problem Set 5Determinants.
Problem Set 6Euclidean Spaces. Orthogonality. Norms.
Problem Set 7Linear Operators. Eigenvalues and Eigenvectors.

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About me

Andrei Antonenko

Lecturer, Department of Linguistics
Stony Brook University

Ph.D. 2012, Stony Brook University

Areas of interest: syntax, semantics, linguistics education

 

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