Linear Algebra

This repository contains notes and assignments related to the MITOPENCOURSEWARE - Linear Algebra

• Instructor: Prof. Gilbert Strang
• MIT Course Number - 18.06
• Course Link: https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/index.html

<p> Course Description: A basic subject on matrix theory and linear algebra. </p>

|#Session|Topic| |---|----------------------------------| | 1 | The geometry of linear equations | | 2 | Elimination with matrices | | 3 | Matrix operations and inverses | | 4 | LU and LDU factorization | | 5 | Transposes and permutations| | 6 | Vector spaces and subspaces| | 7 | The nullspace: Solving Ax = 0 | | 8 | Rectangular PA = LU and Ax = b | | 9 | Row reduced echelon form| | 10 | Basis and dimension | | 11 | The four fundamental subspaces | | 12 | Exam 1: Chapters 1 to 3.4 | | 13 | Graphs and networks | | 14 | Orthogonality | | 15 | Projections and subspaces | | 16 | Least squares approximations | | 17 | Gram-Schmidt and A = QR | | 18 | Properties of determinants | | 19 | Formulas for determinants | | 20 | Applications of determinants | | 21 | Eigenvalues and eigenvectors | | 22 | Diagonalization | | 23 | Markov matrices | | 24 | Review for exam 2 | | 25 | Exam 2: Chapters 1-5, 6.1-6.2, 8.2 | | 26 | Differential equations | | 27 | Symmetric matrices | | 28 | Positive definite matrices | | 29 | Matrices in engineering | | 30 | Similar matrices | | 31 | Singular value decomposition | | 32 | Fourier series, FFT, complex matrices | | 33 | Linear transformations | | 34 | Choice of basis | | 35 | Linear programming | | 36 | Course review | | 37 | Exam 3: Chapters 1-8 (8.1, 2, 3, 5) | | 38 | Numerical linear algebra | | 39 | Computational science | | 40 | Final exam |