06:33

Testing if a subset of a vector space is a subspace, the 2 axioms involved and why

08:09

Subspaces Part 1: definition of a subspace

04:20

Vector space Part 3: definition of a vector space

04:05

Vector spaces Part 2: What makes R^n a "space" continued

04:39

Vector space Part 1: what makes R^n a "space"

03:25

Vector operatorations: addition, subtraction, scalar multiplication, Part 2, algebraic

05:15

Vector operations: addition, subtraction, & scalar multiplication, Part 1, geometric

04:52

What are vectors? Part 4, the Euclidean n-space

02:25

What are vectors? Part 3, components of a vector

04:33

What are vectors? Part 2, vectors in the xOy coordinate system

03:11

What are vectors? Part 1, physical and geometric vectors

30:35

Introduction to Matlab interface and the publishing feature (instructions for labs in MATH 272)

01:56

Example of a linear equation (Breakfast series part 1)

06:50

How to verify & visualize a solution of a linear equation (Breakfast series part 2)

02:24

What is a linear system? A 2 by 2 example. (Breakfast series part 3)

00:55

What is a homogeneous linear equation? (Definition and examples)

04:47

What is a linear system? (Definition and examples)

01:55

What is a homogeneous linear system? The definition.

04:56

What is a linearly independent set?

03:31

Geometric view of linear equations

07:33

What is a linear equation? (Definition and examples)

02:16

Complex eigenvalues and eigenvectors: An Example Part 3

04:56

Complex eigenvalues and eigenvectors: An Example. Part 2

03:22

Complex Eigenvectors: An Example. Part 1

01:40

Complex Eigenvalues and Eigenvectors: complex conjugates

02:02

Linearly independent functions: example

03:16

The rank nullity relation and examples

03:40

linear Independence of functions

02:59

How to find the range of a matrix: example

04:45

How to find the null space and the nullity of a matrix: Example

02:56

Common singular matrices: part 3

00:34

Common singular matrices: part 2

01:32

Common singular matrices: part 1

02:55

2 common confusions about linear systems, augmented matrices, and reduced Echelon forms

03:13

How to multiply two matrices? Is AB = BA for matrices? Example 1.

01:48

How to multiply two matrices? Is AB = BA? Example 2

01:32

What is the scalar product (dot product) of two vectors?

04:41

How to find out if a set of vectors are linearly independent? An example.

03:28

When is vector b a linear combination of vectors v1, v2, and v3? An example.

01:45

What is the connection between linear combinations and linear systems? Part 1

04:56

How to multiply matrices

02:47

Why transpose a matrix? Part 5: how to "symmetrize" a matrix.

02:12

Why transpose a matrix? Part 4: unitary matrices, matrices that preserve the length of a vector.

04:35

Why transpose a matrix? Part 3: scalar products

03:22

Why transpose a matrix? Part 2: symmetric matrices

02:02

Why transpose a matrix? Part 1: the transpose of a transpose

04:05

What is the "span" of a set of vectors?

03:11

What Is A Vector?

05:39

What is a linear combination?

04:36

What Is A Matrix? Example: adjacency matrix of a social network.