EE-Learning
Null space 3: Relation to linear independence
Catogry:
Math
Subject:
Linear Algebra
Course:
Vectors And Spaces
Lecture List
Showing that the candidate basis does span C(A)
Showing relation between basis cols and pivot cols
Dimension of the column space or rank
Dimension of the null space or nullity
Proof: Any subspace basis has same number of elements
Visualizing a column space as a plane in R3
Null space and column space basis
Column space of a matrix
Null space 3: Relation to linear independence
Null space 2: Calculating the null space of a matrix
Introduction to the null space of a matrix
Matrix vector products
Using matrix row-echelon form in order to show a linear system has no solutions
Solving linear systems with matrices
Solving a system of 3 equations and 4 variables using matrix row-echelon form
Distance between planes
Point distance to plane
Normal vector from plane equation
Vector triple product expansion (very optional)
Dot and cross product comparison/intuition
Proof: Relationship between cross product and sin of angle
Cross product introduction
Defining a plane in R3 with a point and normal vector
Defining the angle between vectors
Vector triangle inequality
Proof of the Cauchy-Schwarz inequality
Proving vector dot product properties
Vector dot product and vector length
Basis of a subspace
Linear subspaces
Span and linear independence example
More on linear independence
Introduction to linear independence
Linear combinations and span
Parametric representations of lines
Unit vectors intro
Vector examples
Multiplying a vector by a scalar
Adding vectors algebraically & graphically
Real coordinate spaces
Vector intro for linear algebra