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:

Subspaces of R

Determinants Eigenvalues and Eigenvectors Symmetric Matrices and Quadratic Forms

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****Basic Introduction to MATLAB
Basic Arithmetic
Trigonometry
Logarithms and Exponentials
Variables
Retrieving Variable Values
Saving and Loading
Recording Your Steps
Helpful Links
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****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
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****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
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****Subspaces of R ^{n} and Their
Dimensions
Image
Kernal
Linear Independence
Basis
Dimension
Rank-Nullity Theorem
Coordinates
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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
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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
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****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.