| (16 intermediate revisions by the same user not shown) | |||
| Line 11: | Line 11: | ||
</center> | </center> | ||
---- | ---- | ||
| − | == | + | ==The Basics== |
| − | *[[ | + | *Linear Equations and Linear Transformations |
| + | **Introduction to [[Matrix]] | ||
| + | **[[Matrix Multiplication|Matrix multiplication Version 1]] and [[Matrix_multiplication_MA265F10Walther|Version 2]] | ||
| + | **[[Inverse of a Matrix|Inverse of a Matrix Version 1]] and [[Inverse_MA265F10Walther|Version 2]] | ||
| + | **Introduction to [[Linear transformation|Linear Transformation]]s | ||
| + | * Subspaces of <math>R^n</math> | ||
| + | **Definition of [[Subspace]] | ||
| + | **Definition of [[Kernel (linear algebra)|Kernel]] | ||
| + | **Definition of [[Image (linear algebra)|Image]] | ||
| + | **What is the [[rank_nullity_theorem (linear algebra)|Rank Nullity Theorem]]? | ||
| + | **When are vectors [[Linearly Independent]] | ||
| + | **When do vectors form a [[basis]]? | ||
| + | ***[[Basis%20Explanations%20S13|Supplementary Basis Explanations]] | ||
| + | *Orthogonality | ||
| + | **When are vectors [[orthogonal]]? | ||
| + | *Determinants | ||
| + | **What is a [[determinant]]. | ||
| + | **Another intro to [[On_Determinants|Determinants]] | ||
| + | **What are some [[properties of the determinant]]? | ||
| + | ---- | ||
| + | ==Beyond the Basics== | ||
| + | *[[DimVplusdimVorthisn|Dim(V) + Dim(Vorthogonal)=n]] | ||
| + | *[[Determinant_Transpose_Proof|Proof that transposing a matrix does not change its determinant]] | ||
| + | *[[Inner_Products_MA265F10Walther|Inner products and orthogonality]] | ||
| + | *[[Hint_-_The_Least_Squares_Solution|Least Squares Solution (the formula)]] | ||
| + | *[[Jacobian|Jacobians and their Applications]], by [[Math_squad|Math Squad]] member [[user:ruanj|Joseph Ruan]] | ||
* A tutorial about Bases, by [[Math_squad|Math Squad]] member [[user:ruanj|Joseph Ruan]]: | * A tutorial about Bases, by [[Math_squad|Math Squad]] member [[user:ruanj|Joseph Ruan]]: | ||
| − | **[[Basis_Explanations_S13 | | + | **[[Basis_Explanations_S13 | What is a Basis? (going beyond the introductory level) ]] |
**[[Basis_Problems| Basis Example Problems specifically with polynomials]] | **[[Basis_Problems| Basis Example Problems specifically with polynomials]] | ||
**[[Change_of_Bases| Change of Basis]] | **[[Change_of_Bases| Change of Basis]] | ||
| − | == | + | *[[Linear_programming_MA265F11Walther|Linear Programming]] |
| + | ---- | ||
| + | ==Applications== | ||
| + | *[[ECE637_tomographic_reconstruction_coordinate_rotation_S13_mhossain|Coordinate Rotations]] | ||
| + | *[[ECE662_Whitening_and_Coloring_Transforms_S14_MH|Whitening and coloring transforms]] | ||
| + | *[[Implementation_of_the_Divide_and_Conquer_DFT_via_Matrices|"divide and conquer" Discrete Fourier Transform (DFT)]] | ||
| + | |||
---- | ---- | ||
| − | [[linear_algebra|Back to Linear Algebra]] | + | [[linear_algebra|Back to "Linear Algebra" topic]] |
Latest revision as of 11:25, 27 March 2015
Tutorials and other Learning Material
The Basics
- Linear Equations and Linear Transformations
- Introduction to Matrix
- Matrix multiplication Version 1 and Version 2
- Inverse of a Matrix Version 1 and Version 2
- Introduction to Linear Transformations
- Subspaces of $ R^n $
- Definition of Subspace
- Definition of Kernel
- Definition of Image
- What is the Rank Nullity Theorem?
- When are vectors Linearly Independent
- When do vectors form a basis?
- Orthogonality
- When are vectors orthogonal?
- Determinants
- What is a determinant.
- Another intro to Determinants
- What are some properties of the determinant?
Beyond the Basics
- Dim(V) + Dim(Vorthogonal)=n
- Proof that transposing a matrix does not change its determinant
- Inner products and orthogonality
- Least Squares Solution (the formula)
- Jacobians and their Applications, by Math Squad member Joseph Ruan
- A tutorial about Bases, by Math Squad member Joseph Ruan:
- Linear Programming
Applications
- Coordinate Rotations
- Whitening and coloring transforms
- "divide and conquer" Discrete Fourier Transform (DFT)
