Linear Algebra
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What you'll learn
This course includes
- 35.5 hours of video
- Certificate of completion
- Access on mobile and TV
Course content
1 modules • 143 lessons • 35.5 hours of video
Linear Algebra
143 lessons
• 35.3 hours
Linear Algebra
143 lessons
• 35.3 hours
- Introduction to the inverse of a function | Matrix transformations | Linear Algebra | Khan Academy 18:54
- 3 x 3 determinant | Matrix transformations | Linear Algebra | Khan Academy 10:01
- Exploring the solution set of Ax = b | Matrix transformations | Linear Algebra | Khan Academy 16:34
- Introduction to projections | Matrix transformations | Linear Algebra | Khan Academy 14:37
- Transpose of a matrix | Matrix transformations | Linear Algebra | Khan Academy 08:37
- Determinant when row multiplied by scalar | Matrix transformations | Linear Algebra | Khan Academy 13:20
- Linear transformations | Matrix transformations | Linear Algebra | Khan Academy 13:52
- Rule of Sarrus of determinants | Matrix transformations | Linear Algebra | Khan Academy 07:18
- Deriving a method for determining inverses | Matrix transformations | Linear Algebra | Khan Academy 18:00
- Preimage and kernel example | Matrix transformations | Linear Algebra | Khan Academy 15:23
- Proof: Invertibility implies a unique solution to f(x)=y | Linear Algebra | Khan Academy 22:41
- A more formal understanding of functions | Matrix transformations | Linear Algebra | Khan Academy 16:01
- Transposes of sums and inverses | Matrix transformations | Linear Algebra | Khan Academy 08:40
- Compositions of linear transformations 2 | Matrix transformations | Linear Algebra | Khan Academy 16:31
- Showing that A-transpose x A is invertible | Matrix transformations | Linear Algebra | Khan Academy 12:34
- Visualizations of left nullspace and rowspace | Linear Algebra | Khan Academy 19:50
- n x n determinant | Matrix transformations | Linear Algebra | Khan Academy 18:40
- Matrix product associativity | Matrix transformations | Linear Algebra | Khan Academy 11:59
- Expressing a projection on to a line as a matrix vector prod | Linear Algebra | Khan Academy 16:41
- Matrix condition for one-to-one trans | Matrix transformations | Linear Algebra | Khan Academy 19:59
- Image of a subset under a transformation | Matrix transformations | Linear Algebra | Khan Academy 18:11
- Linear transformations as matrix vector products | Linear Algebra | Khan Academy 17:32
- Relating invertibility to being onto and one-to-one | Linear Algebra | Khan Academy 06:31
- Simpler 4x4 determinant | Matrix transformations | Linear Algebra | Khan Academy 09:13
- Transpose of a matrix product | Matrix transformations | Linear Algebra | Khan Academy 08:50
- Upper triangular determinant | Matrix transformations | Linear Algebra | Khan Academy 08:07
- Determinant when row is added | Matrix transformations | Linear Algebra | Khan Academy 16:55
- (correction) scalar multiplication of row | Matrix transformations | Linear Algebra | Khan Academy 02:52
- Simplifying conditions for invertibility | Matrix transformations | Linear Algebra | Khan Academy 06:37
- More on matrix addition and scalar multiplication | Linear Algebra | Khan Academy 10:42
- Formula for 2x2 inverse | Matrix transformations | Linear Algebra | Khan Academy 18:20
- Determining whether a transformation is onto | Linear Algebra | Khan Academy 25:51
- Compositions of linear transformations 1 | Matrix transformations | Linear Algebra | Khan Academy 12:21
- Determinant as scaling factor | Matrix transformations | Linear Algebra | Khan Academy 20:10
- Vector transformations | Matrix transformations | Linear Algebra | Khan Academy 14:19
- Duplicate row determinant | Matrix transformations | Linear Algebra | Khan Academy 08:19
- Rotation in R3 around the x-axis | Matrix transformations | Linear Algebra | Khan Academy 12:18
- im(T): Image of a transformation | Matrix transformations | Linear Algebra | Khan Academy 16:37
- Determinant after row operations | Matrix transformations | Linear Algebra | Khan Academy 10:25
- Linear transformation examples: Rotations in R2 | Linear Algebra | Khan Academy 17:52
- Unit vectors | Matrix transformations | Linear Algebra | Khan Academy 06:59
- Transpose of a vector | Matrix transformations | Linear Algebra | Khan Academy 12:06
- Showing that inverses are linear | Matrix transformations | Linear Algebra | Khan Academy 21:24
- Determinant and area of a parallelogram | Matrix transformations | Linear Algebra | Khan Academy 21:37
- Determinants along other rows/cols | Matrix transformations | Linear Algebra | Khan Academy 09:03
- Distributive property of matrix products | Matrix transformations | Linear Algebra | Khan Academy 09:52
- Matrix vector products as linear transformations | Linear Algebra | Khan Academy 17:04
- Rowspace and left nullspace | Matrix transformations | Linear Algebra | Khan Academy 23:19
- Linear transformation examples: Scaling and reflections | Linear Algebra | Khan Academy 15:13
- Example of finding matrix inverse | Matrix transformations | Linear Algebra | Khan Academy 06:22
- rank(a) = rank(transpose of a) | Matrix transformations | Linear Algebra | Khan Academy 11:14
- Sums and scalar multiples of linear transformations | Linear Algebra | Khan Academy 15:09
- Determinant of transpose | Matrix transformations | Linear Algebra | Khan Academy 14:10
- Matrix product examples | Matrix transformations | Linear Algebra | Khan Academy 18:14
- Surjective (onto) and injective (one-to-one) functions | Linear Algebra | Khan Academy 09:32
- Preimage of a set | Matrix transformations | Linear Algebra | Khan Academy 05:23
- Matrices to solve a system of equations | Matrices | Precalculus | Khan Academy 16:33
- Matrices: Reduced row echelon form 3 | Vectors and spaces | Linear Algebra | Khan Academy 12:08
- Matrices: Reduced row echelon form 1 | Vectors and spaces | Linear Algebra | Khan Academy 17:43
- Classic video on inverting a 3x3 matrix part 1 | Matrices | Precalculus | Khan Academy 16:45
- Singular matrices | Matrices | Precalculus | Khan Academy 14:27
- Matrices to solve a vector combination problem | Matrices | Precalculus | Khan Academy 14:20
- Idea behind inverting a 2x2 matrix | Matrices | Precalculus | Khan Academy 14:15
- Matrices: Reduced row echelon form 2 | Vectors and spaces | Linear Algebra | Khan Academy 07:37
- Classic video on inverting a 3x3 matrix part 2 | Matrices | Precalculus | Khan Academy 13:36
- Vector triple product expansion (very optional) | Vectors and spaces | Linear Algebra | Khan Academy 14:25
- Normal vector from plane equation | Vectors and spaces | Linear Algebra | Khan Academy 09:58
- Point distance to plane | Vectors and spaces | Linear Algebra | Khan Academy 12:12
- Distance between planes | Vectors and spaces | Linear Algebra | Khan Academy 14:45
- Eigenvalues of a 3x3 matrix | Alternate coordinate systems (bases) | Linear Algebra | Khan Academy 14:08
- Change of basis matrix | Alternate coordinate systems (bases) | Linear Algebra | Khan Academy 17:55
- Finding eigenvectors and eigenspaces example | Linear Algebra | Khan Academy 14:34
- Eigenvectors and eigenspaces for a 3x3 matrix | Linear Algebra | Khan Academy 15:34
- Projections onto subspaces | Linear Algebra | Khan Academy 17:26
- Introduction to orthonormal bases | Linear Algebra | Khan Academy 11:16
- Least squares examples | Alternate coordinate systems (bases) | Linear Algebra | Khan Academy 18:50
- Showing that an eigenbasis makes for good coordinate systems | Linear Algebra | Khan Academy 13:09
- Alternate basis transformation matrix example part 2 | Linear Algebra | Khan Academy 12:36
- Changing coordinate systems to help find a transformation matrix | Linear Algebra | Khan Academy 29:00
- Orthogonal complement of the nullspace | Linear Algebra | Khan Academy 03:27
- Representing vectors in rn using subspace members | Linear Algebra | Khan Academy 27:00
- Least squares approximation | Linear Algebra | Khan Academy 15:32
- Introduction to eigenvalues and eigenvectors | Linear Algebra | Khan Academy 07:43
- Transformation matrix with respect to a basis | Linear Algebra | Khan Academy 18:02
- Orthogonal complements | Alternate coordinate systems (bases) | Linear Algebra | Khan Academy 22:08
- Subspace projection matrix example | Linear Algebra | Khan Academy 13:04
- Another least squares example | Alternate coordinate systems (bases) | Linear Algebra | Khan Academy 13:25
- Finding projection onto subspace with orthonormal basis example | Linear Algebra | Khan Academy 06:42
- Coordinates with respect to orthonormal bases | Linear Algebra | Khan Academy 15:28
- Another example of a projection matrix | Linear Algebra | Khan Academy 21:36
- Gram-Schmidt example with 3 basis vectors | Linear Algebra | Khan Academy 13:57
- Projection is closest vector in subspace | Linear Algebra | Khan Academy 09:05
- A projection onto a subspace is a linear transformation | Linear Algebra | Khan Academy 16:16
- Unique rowspace solution to Ax = b | Linear Algebra | Khan Academy 19:12
- Example using orthogonal change-of-basis matrix to find transformation matrix | Khan Academy 27:04
- Alternate basis transformation matrix example | Linear Algebra | Khan Academy 13:20
- Invertible change of basis matrix | Linear Algebra | Khan Academy 13:34
- dim(v) + dim(orthogonal complement of v) = n | Linear Algebra | Khan Academy 09:27
- Example solving for the eigenvalues of a 2x2 matrix | Linear Algebra | Khan Academy 05:39
- Rowspace solution to Ax = b example | Linear Algebra | Khan Academy 19:38
- The Gram-Schmidt process | Alternate coordinate systems (bases) | Linear Algebra | Khan Academy 19:24
- Proof of formula for determining eigenvalues | Linear Algebra | Khan Academy 09:19
- Gram-Schmidt process example | Alternate coordinate systems (bases) | Linear Algebra | Khan Academy 13:14
- Visualizing a projection onto a plane | Linear Algebra | Khan Academy 09:28
- Coordinates with respect to a basis | Linear Algebra | Khan Academy 16:08
- Projections onto subspaces with orthonormal bases | Linear Algebra | Khan Academy 16:14
- Orthogonal matrices preserve angles and lengths | Linear Algebra | Khan Academy 11:16
- Orthogonal complement of the orthogonal complement | Linear Algebra | Khan Academy 12:18
- Defining the angle between vectors | Vectors and spaces | Linear Algebra | Khan Academy 25:11
- Proof: Relationship between cross product and sin of angle | Linear Algebra | Khan Academy 18:09
- Matrix vector products | Vectors and spaces | Linear Algebra | Khan Academy 21:10
- Span and linear independence example | Vectors and spaces | Linear Algebra | Khan Academy 16:53
- More on linear independence | Vectors and spaces | Linear Algebra | Khan Academy 17:38
- Showing relation between basis cols and pivot cols | Linear Algebra | Khan Academy 08:33
- Showing that the candidate basis does span C(A) | Vectors and spaces | Linear Algebra | Khan Academy 13:40
- Introduction to linear independence | Vectors and spaces | Linear Algebra | Khan Academy 15:46
- Visualizing a column space as a plane in R3 | Vectors and spaces | Linear Algebra | Khan Academy 21:11
- Dimension of the column space or rank | Vectors and spaces | Linear Algebra | Khan Academy 12:48
- Vector triangle inequality | Vectors and spaces | Linear Algebra | Khan Academy 18:53
- Linear combinations and span | Vectors and spaces | Linear Algebra | Khan Academy 20:35
- Defining a plane in R3 with a point and normal vector | Linear Algebra | Khan Academy 13:53
- Vector dot product and vector length | Vectors and spaces | Linear Algebra | Khan Academy 09:10
- Proof: Any subspace basis has same number of elements | Linear Algebra | Khan Academy 21:35
- Null space and column space basis | Vectors and spaces | Linear Algebra | Khan Academy 25:13
- Dimension of the null space or nullity | Vectors and spaces | Linear Algebra | Khan Academy 13:59
- Parametric representations of lines | Vectors and spaces | Linear Algebra | Khan Academy 24:46
- Introduction to the null space of a matrix | Vectors and spaces | Linear Algebra | Khan Academy 10:23
- Cross product introduction | Vectors and spaces | Linear Algebra | Khan Academy 15:47
- Linear subspaces | Vectors and spaces | Linear Algebra | Khan Academy 23:29
- Null space 2: Calculating the null space of a matrix | Linear Algebra | Khan Academy 13:07
- Proof of the Cauchy-Schwarz inequality | Vectors and spaces | Linear Algebra | Khan Academy 16:55
- Vector examples | Vectors and spaces | Linear Algebra | Khan Academy 25:33
- Proving vector dot product properties | Vectors and spaces | Linear Algebra | Khan Academy 10:45
- Column space of a matrix | Vectors and spaces | Linear Algebra | Khan Academy 10:40
- Dot and cross product comparison/intuition | Vectors and spaces | Linear Algebra | Khan Academy 19:14
- Null space 3: Relation to linear independence | Vectors and spaces | Linear Algebra | Khan Academy 11:35
- Basis of a subspace | Vectors and spaces | Linear Algebra | Khan Academy 19:00
- Introduction to matrices 11:51
- Matrix multiplication (part 1) 13:41
- Matrix multiplication (part 2) 14:37
- 3-variable linear equations (part 1) 08:02
- Solving 3 Equations with 3 Unknowns 15:26
- Linear Algebra: Introduction to Vectors 16:31
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