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**Another intro to [[On_Determinants|Determinants]] | **Another intro to [[On_Determinants|Determinants]] | ||
**What are some [[properties of the determinant]]? | **What are some [[properties of the determinant]]? | ||
| + | *The [[Inverse_MA265F10Walther|inverse of a matrix]] | ||
---- | ---- | ||
==Beyond the Basics== | ==Beyond the Basics== | ||
*[[DimVplusdimVorthisn|Dim(V) + Dim(Vorthogonal)=n]] | *[[DimVplusdimVorthisn|Dim(V) + Dim(Vorthogonal)=n]] | ||
*[[Determinant_Transpose_Proof|Proof that transposing a matrix does not change its determinant]] | *[[Determinant_Transpose_Proof|Proof that transposing a matrix does not change its determinant]] | ||
| − | *[[Hint_-_The_Least_Squares_Solution|Least Squares Solution | + | *[[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]] | *[[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]]: | ||
Revision as of 21:41, 4 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
- 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?
- The inverse of a matrix
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
Click HERE to view all pages in the "linear algebra" Category
