Linear Algebra
by Khan Academy
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Description
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 this with regular high school algebra.
| Name | Description | Released | Price | ||
|---|---|---|---|---|---|
| 1 | VideoIntroduction to matrices | -- | 8/21/10 | Free | View In iTunes |
| 2 | VideoMatrix multiplication (part 1) | -- | 8/21/10 | Free | View In iTunes |
| 3 | VideoMatrix multiplication (part 2) | -- | 8/21/10 | Free | View In iTunes |
| 4 | VideoInverse Matrix (part 1) | -- | 8/21/10 | Free | View In iTunes |
| 5 | VideoInverting matrices (part 2) | -- | 8/21/10 | Free | View In iTunes |
| 6 | VideoInverting Matrices (part 3) | -- | 8/21/10 | Free | View In iTunes |
| 7 | VideoMatrices to solve a system of equations | -- | 8/21/10 | Free | View In iTunes |
| 8 | VideoMatrices to solve a vector combination problem | -- | 8/21/10 | Free | View In iTunes |
| 9 | VideoLinear Algebra: Eigenvalues of a 3x3 matrix | -- | 8/21/10 | Free | View In iTunes |
| 10 | VideoSingular Matrices | -- | 8/21/10 | Free | View In iTunes |
| 11 | Video3-variable linear equations (part 1) | -- | 8/21/10 | Free | View In iTunes |
| 12 | VideoSolving 3 Equations with 3 Unknowns | -- | 8/21/10 | Free | View In iTunes |
| 13 | VideoLinear Algebra: Eigenvectors and Eigenspaces for a 3x3 matrix | -- | 8/21/10 | Free | View In iTunes |
| 14 | VideoLin Alg: Showing that A-transpose x A is invertible | -- | 8/21/10 | Free | View In iTunes |
| 15 | VideoLin Alg: Alternate Basis Tranformation Matrix Example Part 2 | -- | 8/21/10 | Free | View In iTunes |
| 16 | VideoLin Alg: Alternate Basis Tranformation Matrix Example | -- | 8/21/10 | Free | View In iTunes |
| 17 | VideoLinear Algebra: Basis of a Subspace | -- | 8/21/10 | Free | View In iTunes |
| 18 | VideoShowing that the candidate basis does span C(A) | -- | 8/21/10 | Free | View In iTunes |
| 19 | VideoProof of the Cauchy-Schwarz Inequality | -- | 8/21/10 | Free | View In iTunes |
| 20 | VideoLin Alg: Changing coordinate systems to help find a transformation matrix | -- | 8/21/10 | Free | View In iTunes |
| 21 | VideoLinear Algebra: Change of Basis Matrix | -- | 8/21/10 | Free | View In iTunes |
| 22 | VideoVisualizing a Column Space as a Plane in R3 | -- | 8/21/10 | Free | View In iTunes |
| 23 | VideoColumn Space of a Matrix | -- | 8/21/10 | Free | View In iTunes |
| 24 | VideoNull Space and Column Space Basis | -- | 8/21/10 | Free | View In iTunes |
| 25 | VideoCompositions of Linear Transformations 1 | -- | 8/21/10 | Free | View In iTunes |
| 26 | VideoCompositions of Linear Transformations 2 | -- | 8/21/10 | Free | View In iTunes |
| 27 | VideoLinear Algebra: Deriving a method for determining inverses | -- | 8/21/10 | Free | View In iTunes |
| 28 | VideoLinear Algebra: Coordinates with Respect to a Basis | -- | 8/21/10 | Free | View In iTunes |
| 29 | VideoLinear Algebra: Cross Product Introduction | -- | 8/21/10 | Free | View In iTunes |
| 30 | VideoProof: Relationship between cross product and sin of angle | -- | 8/21/10 | Free | View In iTunes |
| 31 | VideoLinear Algebra: Determinant after row operations | -- | 8/21/10 | Free | View In iTunes |
| 32 | VideoLinear Algebra: Upper Triangular Determinant | -- | 8/21/10 | Free | View In iTunes |
| 33 | VideoLinear Algebra: Formula for 2x2 inverse | -- | 8/21/10 | Free | View In iTunes |
| 34 | VideoLinear Algebra: 3x3 Determinant | -- | 8/21/10 | Free | View In iTunes |
| 35 | VideoLinear Algebra: nxn Determinant | -- | 8/21/10 | Free | View In iTunes |
| 36 | VideoLinear Algebra: Determinants along other rows/cols | -- | 8/21/10 | Free | View In iTunes |
| 37 | VideoLinear Algebra: Rule of Sarrus of Determinants | -- | 8/21/10 | Free | View In iTunes |
| 38 | VideoLinear Algebra: Determinant when row multiplied by scalar | -- | 8/21/10 | Free | View In iTunes |
| 39 | VideoLinear Algebra: (correction) scalar muliplication of row | -- | 8/21/10 | Free | View In iTunes |
| 40 | VideoLinear Algebra: Determinant when row is added | -- | 8/21/10 | Free | View In iTunes |
| 41 | VideoLinear Algebra: Duplicate Row Determinant | -- | 8/21/10 | Free | View In iTunes |
| 42 | VideoLinear Algebra: Determinant and area of a parallelogram | -- | 8/21/10 | Free | View In iTunes |
| 43 | VideoLinear Algebra: Determinant as Scaling Factor | -- | 8/21/10 | Free | View In iTunes |
| 44 | VideoLinear Algebra: Determinant of Transpose | -- | 8/21/10 | Free | View In iTunes |
| 45 | VideoProof: Any subspace basis has same number of elements | -- | 8/21/10 | Free | View In iTunes |
| 46 | VideoLinear Algebra: dim(V) + dim(orthogonoal complelent of V)=n | -- | 8/21/10 | Free | View In iTunes |
| 47 | VideoDot and Cross Product Comparison/Intuition | -- | 8/21/10 | Free | View In iTunes |
| 48 | VideoVector Dot Product and Vector Length | -- | 8/21/10 | Free | View In iTunes |
| 49 | VideoProving Vector Dot Product Properties | -- | 8/21/10 | Free | View In iTunes |
| 50 | VideoLinear Algebra: Showing that an eigenbasis makes for good coordinate systems | -- | 8/21/10 | Free | View In iTunes |
| 51 | VideoLinear Algebra: Introduction to Eigenvalues and Eigenvectors | -- | 8/21/10 | Free | View In iTunes |
| 52 | VideoLinear Algebra: Proof of formula for determining Eigenvalues | -- | 8/21/10 | Free | View In iTunes |
| 53 | VideoLinear Algebra: Example solving for the eigenvalues of a 2x2 matrix | -- | 8/21/10 | Free | View In iTunes |
| 54 | VideoLinear Algebra: Finding Eigenvectors and Eigenspaces example | -- | 8/21/10 | Free | View In iTunes |
| 55 | VideoA more formal understanding of functions | -- | 8/21/10 | Free | View In iTunes |
| 56 | VideoLinear Algebra: The Gram-Schmidt Process | -- | 8/21/10 | Free | View In iTunes |
| 57 | VideoLinear Algebra: Gram-Schmidt Process Example | -- | 8/21/10 | Free | View In iTunes |
| 58 | VideoLinear Algebra: Gram-Schmidt example with 3 basis vectors | -- | 8/21/10 | Free | View In iTunes |
| 59 | VideoSpan and Linear Independence Example | -- | 8/21/10 | Free | View In iTunes |
| 60 | Videoim(T): Image of a Transformation | -- | 8/21/10 | Free | View In iTunes |
| 61 | VideoLinear Algebra: Matrix condition for one-to-one trans | -- | 8/21/10 | Free | View In iTunes |
| 62 | VideoLinear Algebra: Showing that Inverses are Linear | -- | 8/21/10 | Free | View In iTunes |
| 63 | VideoLin Alg: Invertible Change of Basis Matrix | -- | 8/21/10 | Free | View In iTunes |
| 64 | VideoPreimage and Kernel Example | -- | 8/21/10 | Free | View In iTunes |
| 65 | VideoLinear Algebra: Least Squares Examples | -- | 8/21/10 | Free | View In iTunes |
| 66 | VideoLinear Algebra: Another Least Squares Example | -- | 8/21/10 | Free | View In iTunes |
| 67 | VideoLinear Algebra: Least Squares Approximation | -- | 8/21/10 | Free | View In iTunes |
| 68 | VideoLinear Algebra: Introduction to Vectors | -- | 8/21/10 | Free | View In iTunes |
| 69 | VideoLinear Algebra: Introduction to Linear Independence | -- | 8/21/10 | Free | View In iTunes |
| 70 | VideoMore on linear independence | -- | 8/21/10 | Free | View In iTunes |
| 71 | VideoLinear Transformations | -- | 8/21/10 | Free | View In iTunes |
| 72 | VideoMore on Matrix Addition and Scalar Multiplication | -- | 8/21/10 | Free | View In iTunes |
| 73 | VideoMatrix Product Associativity | -- | 8/21/10 | Free | View In iTunes |
| 74 | VideoDistributive Property of Matrix Products | -- | 8/21/10 | Free | View In iTunes |
| 75 | VideoLinear Algebra: Example of Finding Matrix Inverse | -- | 8/21/10 | Free | View In iTunes |
| 76 | VideoLinear Algebra: Matrix Product Examples | -- | 8/21/10 | Free | View In iTunes |
| 77 | VideoLinear Transformations as Matrix Vector Products | -- | 8/21/10 | Free | View In iTunes |
| 78 | VideoMatrix Vector Products as Linear Transformations | -- | 8/21/10 | Free | View In iTunes |
| 79 | VideoMatrix Vector Products | -- | 8/21/10 | Free | View In iTunes |
| 80 | VideoLinear Algebra: Exploring the solution set of Ax=b | -- | 8/21/10 | Free | View In iTunes |
| 81 | VideoDefining a plane in R3 with a point and normal vector | -- | 8/21/10 | Free | View In iTunes |
| 82 | VideoDimension of the Null Space or Nullity | -- | 8/21/10 | Free | View In iTunes |
| 83 | VideoNull Space 2: Calculating the null space of a matrix | -- | 8/21/10 | Free | View In iTunes |
| 84 | VideoNull Space 3: Relation to Linear Independence | -- | 8/21/10 | Free | View In iTunes |
| 85 | VideoDetermining whether a transformation is onto | -- | 8/21/10 | Free | View In iTunes |
| 86 | VideoLin Alg: Representing vectors in Rn using subspace members | -- | 8/21/10 | Free | View In iTunes |
| 87 | VideoLinear Algebra: Orthogonal Complements | -- | 8/21/10 | Free | View In iTunes |
| 88 | VideoLin Alg: Example using orthogonal change-of-basis matrix to find transformation matrix | -- | 8/21/10 | Free | View In iTunes |
| 89 | VideoLin Alg: Orthogonal matrices preserve angles and lengths | -- | 8/21/10 | Free | View In iTunes |
| 90 | VideoLinear Algebra: Introduction to Orthonormal Bases | -- | 8/21/10 | Free | View In iTunes |
| 91 | VideoLinear Algebra: Coordinates with respect to orthonormal bases | -- | 8/21/10 | Free | View In iTunes |
| 92 | VideoLin Alg: Projections onto subspaces with orthonormal bases | -- | 8/21/10 | Free | View In iTunes |
| 93 | VideoLin Alg: Finding projection onto subspace with orthonormal basis example | -- | 8/21/10 | Free | View In iTunes |
| 94 | VideoLinear Algebra: Parametric Representations of Lines | -- | 8/21/10 | Free | View In iTunes |
| 95 | VideoShowing relation between basis cols and pivot cols | -- | 8/21/10 | Free | View In iTunes |
| 96 | VideoPreimage of a set | -- | 8/21/10 | Free | View In iTunes |
| 97 | VideoLinear Alg: Projection is closest vector in subspace | -- | 8/21/10 | Free | View In iTunes |
| 98 | VideoLin Alg: Another Example of a Projection Matrix | -- | 8/21/10 | Free | View In iTunes |
| 99 | VideoLinear Algebra: Subspace Projection Matrix Example | -- | 8/21/10 | Free | View In iTunes |
| 100 | VideoIntroduction to Projections | -- | 8/21/10 | Free | View In iTunes |
| 101 | VideoExpressing a Projection on to a line as a Matrix Vector prod | -- | 8/21/10 | Free | View In iTunes |
| 102 | VideoRotation in R3 around the X-axis | -- | 8/21/10 | Free | View In iTunes |
| 103 | VideoDimension of the Column Space or Rank | -- | 8/21/10 | Free | View In iTunes |
| 104 | VideoLinear Algebra: Rank(A) = Rank(transpose of A) | -- | 8/21/10 | Free | View In iTunes |
| 105 | Videor3rotation_640 | -- | 8/22/10 | Free | View In iTunes |
| 106 | Videorank1_640 | -- | 8/22/10 | Free | View In iTunes |
| 107 | Videoranktranspose_640 | -- | 8/22/10 | Free | View In iTunes |
| 108 | VideoLinear Transformation Examples: Rotations in R2 | -- | 8/22/10 | Free | View In iTunes |
| 109 | VideoLinear Algebra: Rowspace and Left Nullspace | -- | 8/22/10 | Free | View In iTunes |
| 110 | VideoLin Alg: Orthogonal Complement of the Nullspace | -- | 8/22/10 | Free | View In iTunes |
| 111 | VideoLin Alg: Unique rowspace solution to Ax=b | -- | 8/22/10 | Free | View In iTunes |
| 112 | VideoLinear Alg: Rowspace Solution to Ax=b example | -- | 8/22/10 | Free | View In iTunes |
| 113 | VideoMatrices: Reduced Row Echelon Form 2 | -- | 8/22/10 | Free | View In iTunes |
| 114 | VideoMatrices: Reduced Row Echelon Form 3 | -- | 8/22/10 | Free | View In iTunes |
| 115 | VideoMatrices: Reduced Row Echelon Form 1 | -- | 8/22/10 | Free | View In iTunes |
| 116 | VideoLinear Algebra: Simplifying conditions for invertibility | -- | 8/22/10 | Free | View In iTunes |
| 117 | VideoLinear Combinations and Span | -- | 8/22/10 | Free | View In iTunes |
| 118 | VideoLinear Subspaces | -- | 8/22/10 | Free | View In iTunes |
| 119 | VideoLinear Algebra: Projections onto Subspaces | -- | 8/22/10 | Free | View In iTunes |
| 120 | VideoLinear Alg: Visualizing a projection onto a plane | -- | 8/22/10 | Free | View In iTunes |
| 121 | VideoLin Alg: A Projection onto a Subspace is a Linear Transforma | -- | 8/22/10 | Free | View In iTunes |
| 122 | VideoSurjective (onto) and Injective (one-to-one) functions | -- | 8/22/10 | Free | View In iTunes |
| 123 | VideoRelating invertibility to being onto and one-to-one | -- | 8/22/10 | Free | View In iTunes |
| 124 | VideoImage of a subset under a transformation | -- | 8/22/10 | Free | View In iTunes |
| 125 | VideoLin Alg: Transformation Matrix with Respect to a Basis | -- | 8/22/10 | Free | View In iTunes |
| 126 | VideoLinear Algebra: Transpose of a Matrix | -- | 8/22/10 | Free | View In iTunes |
| 127 | VideoLinear Algebra: Transposes of sums and inverses | -- | 8/22/10 | Free | View In iTunes |
| 128 | VideoLinear Algebra: Vector Triangle Inequality | -- | 8/22/10 | Free | View In iTunes |
| 129 | VideoProof: Invertibility implies a unique solution to f(x)=y | -- | 8/22/10 | Free | View In iTunes |
| 130 | VideoUnit Vectors | -- | 8/22/10 | Free | View In iTunes |
| 131 | VideoDefining the angle between vectors | -- | 8/22/10 | Free | View In iTunes |
| 132 | VideoLinear Algebra: Vector Examples | -- | 8/22/10 | Free | View In iTunes |
| 133 | VideoVector Transformations | -- | 8/22/10 | Free | View In iTunes |
| 134 | VideoLinear Algebra: Transpose of a Vector | -- | 8/22/10 | Free | View In iTunes |
| 135 | VideoLin Alg: Visualizations of Left Nullspace and Rowspace | -- | 8/22/10 | Free | View In iTunes |
| 136 | VideoLin Alg: Orthogonal Complement of the Orthogonal Complement | -- | 8/22/10 | Free | View In iTunes |
| Total: 136 Episodes |
Customer Reviews
Gaps in sequence
Just noticing that the playlists contain gaps and may be out of order. If this could be fixed we'd have a fantastic series of Lin algebra tutorials. I learned this subject at university in England but never understood it at this depth. Thank you Sal. A lifelong learner!
Video is clipped -- so frustrating and nearly useless...
The video "blackboard" as reproduced on iPad, iPhone, and on my computer via ITunes is clipped both vertically and horizontally. The vertical clipping is the worst so as the lecturer "writes" on the bottom part of the board it is mostly not visible. How could this be allowed on iTunes? Yes, it's free, but surely there are standards for these academic videos, right? Very disappointing...
This review is for the first episode only. Hopefully subsequent epsiodes have this problem corrected. If so, I'll amend thisreview.
Test scores have gone up!!!
Khan is fantastic at simplifying the most complex problems into easy to see pieces. My performance in class has greatly improved since I started watching these!
