UQ-Linear Algebra

Juan Carlos Ponce Campuzano, Nov 3, 2016

Table of Contents

  1. Systems of equations
    1. Systems of linear equations
    2. Vector properties and basic operations
  2. Linear transformations
    1. Basic linear transformations
    2. Geometric properties of matrices
    3. Geometric interpretation of linear transformations
    4. Eigenvalues & Eigenvectors calculator
    5. Matrix transformations 3D
  3. Quadratic forms
    1. Activity: Quadratic forms

1.

Systems of equations

  • 1. Systems of linear equations
  • 2. Vector properties and basic operations

1.1.

Systems of linear equations

– Juan Carlos Ponce Campuzano

1.2.

–

2.

Linear transformations

  • 1. Basic linear transformations
  • 2. Geometric properties of matrices
  • 3. Geometric interpretation of linear transformations
  • 4. Eigenvalues & Eigenvectors calculator
  • 5. Matrix transformations 3D

2.1.

Basic linear transformations

– Juan Carlos Ponce Campuzano

2.2.

–

2.3.

–

2.4.

–

2.5.

–

3.

Quadratic forms

  • 1. Activity: Quadratic forms

3.1.

Activity: Quadratic forms

Consider the quadratic equation of the form [math]ax^2+bxy+cy^2+dx+ey+f=0[/math], where [math]a,b,c,d,e,f\in\mathbb{R}[/math]. Graphs of quadratic equations are known as[b] conic sections.[/b] By means of a rotation of the plane about the origin, a translation of the plane, or both, it is possible to represent every conic in a simplified standard, or canonical, form.[br][br]With the following simulation you can observe the rotation and translation of the axes in order to put a conic in standard position. It also provides the equation of the conic in the final coordinate system. [br][br]
– Juan Carlos Ponce Campuzano

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