The focus of this channel is to provide a basic understanding of Linear Algebra of finite dimensional vector spaces.

Math 2.11.5. Determinants and proof of row-wise linearity
4:01
Math 2.11.5. Determinants and proof of row-wise linearity
Math 2.11.6. Gauss-Jordan elimination and determinants
8:56
Math 2.11.6. Gauss-Jordan elimination and determinants
Math 2.11.7. Determinant and effect of Gauss-Jordan elimination
2:26
Math 2.11.7. Determinant and effect of Gauss-Jordan elimination
Math 2.11.8: Determinant and invertibility
4:05
Math 2.11.8: Determinant and invertibility
Math 2.11.9: Theorem det(AB)=det(A).det(B) and corollaries
3:17
Math 2.11.9: Theorem det(AB)=det(A).det(B) and corollaries
Math 2.11.10 proof of det(AB)=det(A).det(B)
3:54
Math 2.11.10 proof of det(AB)=det(A).det(B)
Math 2.11.11. Laplace expansion of det(A)
9:25
Math 2.11.11. Laplace expansion of det(A)
Math 2.11.12. Cramer's Rule for solving linear systems, application
7:02
Math 2.11.12. Cramer's Rule for solving linear systems, application
Math 2.11.13 Cramer's rule, proof using linearity of det(A)
3:01
Math 2.11.13 Cramer's rule, proof using linearity of det(A)
Math 2.11.14. Determinant of transformation matrix as expansion factor
8:14
Math 2.11.14. Determinant of transformation matrix as expansion factor
Math 2.11.4. Determinant properties, row and column linearity
2:46
Math 2.11.4. Determinant properties, row and column linearity
Math 2.11.3: Determinants examples for stylized cases
9:20
Math 2.11.3: Determinants examples for stylized cases
Math 2.11.2. Definition det(A) for general nxn matrix A
10:52
Math 2.11.2. Definition det(A) for general nxn matrix A
Math 2.11.1: Definition of det(A) where A is 3x3 matrix
7:10
Math 2.11.1: Definition of det(A) where A is 3x3 matrix
Math 2.10.8: Matrix describing change of arbitrary (non-standard unit) bases
3:44
Math 2.10.8: Matrix describing change of arbitrary (non-standard unit) bases
Math 2.10.7: Example change of basis, projection
4:47
Math 2.10.7: Example change of basis, projection
Math 2.10.5: Change of basis, formally
5:34
Math 2.10.5: Change of basis, formally
Math 2.10.4: Transformation matrix, different bases
4:30
Math 2.10.4: Transformation matrix, different bases
Math 2.10.2. Properties of coordinates, algebra
4:24
Math 2.10.2. Properties of coordinates, algebra
Math 2.10.1. Coordinates with respect to basis
4:16
Math 2.10.1. Coordinates with respect to basis
Math 2.10.6: Example change of basis, calculations
4:52
Math 2.10.6: Example change of basis, calculations
Math 2.10.3: Coordinates examples
3:20
Math 2.10.3: Coordinates examples
Math 2.9.6: Span linear (in)dependence and dimension, proof theorem 2.9.5
6:41
Math 2.9.6: Span linear (in)dependence and dimension, proof theorem 2.9.5
Math 2.9.8. Rank nullity theorem
4:07
Math 2.9.8. Rank nullity theorem
Math 2.9.7: Example dimension ker(A)
7:37
Math 2.9.7: Example dimension ker(A)
Math 2.9.2: Number of elements needed for span
3:41
Math 2.9.2: Number of elements needed for span
Math 2.9.5: Span, linear dependence and dimension
2:04
Math 2.9.5: Span, linear dependence and dimension
Math 2.9.4: Number of elements in a basis of subspace in Rn
2:28
Math 2.9.4: Number of elements in a basis of subspace in Rn
Math 2.9.3: Number of elements needed for span, theorem proof
3:11
Math 2.9.3: Number of elements needed for span, theorem proof
Math 2.9.1: Number of elements for span
3:05
Math 2.9.1: Number of elements for span