Linear Algebra

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Matrices, vectors, vector spaces, transformations. Covers all topics in a first year college linear algebra course. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse th…

Khan Academy

Aug 22, 2010 LATEST EPISODE
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Latest episodes from Linear Algebra

Lin Alg: Orthogonal Complement of the Orthogonal Complement

Play Episode Listen Later Aug 22, 2010 12:17

complement orthogonal

Lin Alg: Visualizations of Left Nullspace and Rowspace

Play Episode Listen Later Aug 22, 2010 19:49

left visualizations nullspace

Linear Algebra: Transpose of a Vector

Play Episode Listen Later Aug 22, 2010 12:06

vector linear algebra transpose

Vector Transformations

Play Episode Listen Later Aug 22, 2010 14:18

transformations vector

Linear Algebra: Vector Examples

Play Episode Listen Later Aug 22, 2010 25:33

vector linear algebra

Defining the angle between vectors

Play Episode Listen Later Aug 22, 2010 25:10

defining angle vectors

Unit Vectors

Play Episode Listen Later Aug 22, 2010 6:58

Proof: Invertibility implies a unique solution to f(x)=y

Play Episode Listen Later Aug 22, 2010 22:40

unique solution proof implies

Linear Algebra: Vector Triangle Inequality

Play Episode Listen Later Aug 22, 2010 18:52

triangle inequality vector linear algebra

Linear Algebra: Transposes of sums and inverses

Play Episode Listen Later Aug 22, 2010 8:40

sums linear algebra inverses

Linear Algebra: Transpose of a Matrix

Play Episode Listen Later Aug 22, 2010 8:36

matrix linear algebra transpose

Lin Alg: Transformation Matrix with Respect to a Basis

Play Episode Listen Later Aug 22, 2010 18:01

transformation respect matrix basis

Image of a subset under a transformation

Play Episode Listen Later Aug 22, 2010 18:10

transformation subset

Relating invertibility to being onto and one-to-one

Play Episode Listen Later Aug 22, 2010 6:30

relating one to one

Surjective (onto) and Injective (one-to-one) functions

Play Episode Listen Later Aug 22, 2010 9:31

functions one to one

Lin Alg: A Projection onto a Subspace is a Linear Transforma

Play Episode Listen Later Aug 22, 2010 16:15

projections transforma linear subspace

Linear Alg: Visualizing a projection onto a plane

Play Episode Listen Later Aug 22, 2010 9:27

plane projections linear visualizing

Linear Algebra: Projections onto Subspaces

Play Episode Listen Later Aug 22, 2010 17:25

projections linear algebra

Linear Subspaces

Play Episode Listen Later Aug 22, 2010 23:28

Linear Combinations and Span

Play Episode Listen Later Aug 22, 2010 20:34

linear combinations span

Linear Algebra: Simplifying conditions for invertibility

Play Episode Listen Later Aug 22, 2010 6:36

conditions simplifying linear algebra

Matrices: Reduced Row Echelon Form 1

Play Episode Listen Later Aug 22, 2010 17:42

reduced echelon matrices

Matrices: Reduced Row Echelon Form 3

Play Episode Listen Later Aug 22, 2010 12:07

reduced echelon matrices

Matrices: Reduced Row Echelon Form 2

Play Episode Listen Later Aug 22, 2010 7:36

reduced echelon matrices

Linear Alg: Rowspace Solution to Ax=b example

Play Episode Listen Later Aug 22, 2010 19:37

solution linear

Lin Alg: Unique rowspace solution to Ax=b

Play Episode Listen Later Aug 22, 2010 19:11

unique solution

Lin Alg: Orthogonal Complement of the Nullspace

Play Episode Listen Later Aug 22, 2010 3:26

complement orthogonal nullspace

Linear Algebra: Rowspace and Left Nullspace

Play Episode Listen Later Aug 22, 2010 23:18

left linear algebra nullspace

Linear Transformation Examples: Rotations in R2

Play Episode Listen Later Aug 22, 2010 17:51

transformation linear rotations

ranktranspose_640

Play Episode Listen Later Aug 22, 2010 11:13

rank1_640

Play Episode Listen Later Aug 22, 2010 12:47

r3rotation_640

Play Episode Listen Later Aug 22, 2010 12:17

Linear Algebra: Rank(A) = Rank(transpose of A)

Play Episode Listen Later Aug 21, 2010 11:13

rank linear algebra transpose

Dimension of the Column Space or Rank

Play Episode Listen Later Aug 21, 2010 12:47

space rank dimension column

Rotation in R3 around the X-axis

Play Episode Listen Later Aug 21, 2010 12:17

Expressing a Projection on to a line as a Matrix Vector prod

Play Episode Listen Later Aug 21, 2010 16:40

matrix projections prod vector

Introduction to Projections

Play Episode Listen Later Aug 21, 2010 14:36

Linear Algebra: Subspace Projection Matrix Example

Play Episode Listen Later Aug 21, 2010 13:03

matrix projections subspace linear algebra

Lin Alg: Another Example of a Projection Matrix

Play Episode Listen Later Aug 21, 2010 21:35

matrix projections

Linear Alg: Projection is closest vector in subspace

Play Episode Listen Later Aug 21, 2010 9:04

projections linear vector closest subspace

Preimage of a set

Play Episode Listen Later Aug 21, 2010 5:22

Showing relation between basis cols and pivot cols

Play Episode Listen Later Aug 21, 2010 8:32

showing pivot basis relation cols

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