presented by the JHU Department of Mathematics


Objective:
MATLAB is a very powerful computational program for computers which has its roots in Linear Algebra. We hope that by reading through the help files and trying some of the exercises on your own, MATLAB can become a helpful tool for both your current assignments and studying in Linear Algebra, and also for any future mathematics or engineering classes you may take.

Please click on your desired chapter to scroll down and see a list of topics in that chapter:
Basis Introduction to MATLAB Linear Equations Linear Transformations
Subspaces of Rn and Their Dimension Linear Spaces Orthogonality and Least Squares
Determinants Eigenvalues and Eigenvectors Symmetric Matrices and Quadratic Forms

 

Basic Introduction to MATLAB
Basic Arithmetic Trigonometry Logarithms and Exponentials Variables
Retrieving Variable Values Saving and Loading Recording Your Steps Helpful Links

 

Linear Equations
Creating a Matrix Substituting Within a Symbolic Matrix Manipulating Regular Matrices Vectors
Scalar Multiplication Addition of Matrices Gauss-Jordan Elimination Reduced Row-Echelon Form
Dot Product Rank Number of Solutions

Linear Transformations
Identity Matrix Inverse Matrix Product of a Matrix and a Vector Roations
Rotation-Dilations Orthogonal Projections Reflections Determinant and Inverse of a 2x2 Matrix
Matrix Products

Subspaces of Rn and Their Dimensions
Image Kernal Linear Independence Basis
Dimension Rank-Nullity Theorem Coordinates

Linear Spaces

Orthogonality and Least Squares
Orthogonal Vectors Norm Unit Vector Orthonormal Vectors
Orthogonal Complement Orthogonal Projection Cauchy-Schwarz Inequality Angle Between Two Vectors
Gram-Schmidt Process QR Factorialization Transpose Symmetric and Skew-symmetric Matrices
Orthogonal Matrices Least Squares Solutions Matrix of an Orthogonal Projection



Determinants
Calculating the Determinant Determinants of Special Matrices Determinats of Manipulated Matrices Invertibility
Cramer's Rule



Eigenvalues and Eigenvectors
Characteristic Polynomial Calculating Eigenvalues Calculating Eigenvectors

Symmetric Matrices and Quadratic Forms
Orthogonally Diagonalizable Symmetric Matrices and Eigenvalues How to Orthogonally Diagonalize Quadratic Forms
Definiteness Principal Axes Ellipses and Hyperbolas

 

Supported by Kenan Grant
Copyright 2004: The Johns Hopkins University. All rights reserved.