* D003x.1 Applications of Linear Algebra (Part 1)
- Gain an overview perspective of applications of linear algebra
- Be able to distinguish between linear and nonlinear equations
- Learn terminology of related to matrices
- Learn an algorithm that uses a matrix to visually approximate an image using ASCII characters.
Online app to create ASCII images
will gain an appreciation for how linear processes can model or approximation the world. We will also look specifically at wireframe models that create 3D models.In this unit, you will learn the following:
- To compute matrix addition
- To compute scalar multiplication
- To compute a convex combination of matrices
- Image manipulation using matrix arithmetic
online app for Inversion online online app to Combine pictures online app to generate blending gifs make animation from gif images sequence
To combine two images with matrix arithmetic αA+(1-α)B to adapt the ideas of the last section to create an animation.In this unit, you will learn the following:
- To compute the Euclidean norm on vectors
- To compute the taxicab norm on vectors
- An application of vector norms to data mining for movie recommendations
- An application of vector norms to reading handwritten numbers
- How to compute the Euclidean norm
- How to compute the taxicab norm
- How to apply vector norms to data mining in the context of a movie recommendation system
- How to apply vector norms to compare images
- An algorithm for identify handwritten digits
- To multiply two vectors
- To find the dot product between two vectors
- To find the angle between two vectors
- An application of the dot product to data mining for movie recommendations
- To multiply two matrices
- When multiplication cannot be performed between two matrices
- How to rotate, translate, and reflect points with matrix multiplication
- Applications of matrix multiplication to image creation and manipulation
Spinograph application Transformation
How to multiply two vectors How to compute the dot product of two vectors How to find the angle between two vectors How to apply the dot product to data mining in the context of a movie recommendation system How to multiply two matrices When two matrices cannot be multiplied How to use matrix multiplication to rotate a point about the origin A way to create an image by rotating points with matrix multiplication How to apply vector norms to data mining in the context of a movie recommendation system How to convert a Cartesian coordinate to a homogeneous coordinate (x,y) = (u*x,u*y,u) (1,3) = (1,3,1) (1,3) = (2,6,2) How to convert a homogeneous coordinate to a Cartesian coordinate How to rotate, translate, and reflect homogeneous coordinates with matrix multiplication An application of rotation, translation and reflection to the artwork of puzzle master Scott KimTo solve a system of linear equations The three elementary row operations used to solve linear systems An application of two of the elementary row operations to image manipulation Two encryption methods that utilize linear algebra
How matrix methods date back to 200 BC How to solve systems of linear equations There are 3 operations that allow us to move from one lineas system to another. The three elementary row operations used to solve a linear system.- Switch any 2 rows
- multiply any row with non-zero scalar
- replacing a row by the sum of a non-zero scalar multiple of that row and another row.
An application of two of the elementary row operations to image manipulation
http://math365.org/lifeislinear/Flip/Flip.html http://math365.org/lifeislinear/RowMult/RowMult.html http://math365.org/lifeislinear/CaesarDecode/CaesarDecode.html- A method of encryption that uses matrices
- The inverse of a matrix and how to use it to solve linear systems