Linear Vector Spaces - Linear Algebra
18
22 hrs
$ 8.58
MTH 202: Mathematical Methods IIComprehensive treatise of advanced mathematics covering vector calculus, complex numbers, linear vector spaces, linear maps, matrices, eigenvalues and eigenvectors.
Curated for second-year students of engineering and physical sciences at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.
Comprehensive treatise of advanced mathematics covering vector calculus, complex numbers, linear vector spaces, linear maps, matrices, eigenvalues and eigenvectors. Curated for second-year students of engineering and physical sciences at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.
Course Chapters
1Introduction
Definition of a space, linear vector space, with examples.
Chapter lessons
2.Axioms, conjectures, theorems, etc.29:34
2Vector Subspaces
Definition and examples of linear vector subspaces.
Chapter lessons
3Linear Combinations and Spans
Linear combinations of two or more vectors and linear spans of vector spaces.
Chapter lessons
4Linear Dependence and Independence
Linear dependence and independence of vectors in a vector space.
Chapter lessons
1.Definition18:57
Meaning of linear dependence and independence of vectors in a vector space.
2.Worked examples (1)46:21
Worked examples on linear dependence and independence of vectors in a vector space.
3.Worked examples (2)43:46
More worked examples on linear dependence and independence of vectors in a vector space.
4.Worked examples (3)28:23
More worked examples on linear dependence and independence of vectors in a vector space.
5Basis and Dimension
Basis and dimension of linear vector spaces.
Chapter lessons
1.Definition12:52
Meaning of basis and dimension of a vector space.
2.Worked examples (1)1:19:14
Worked examples on basis and dimension of vector spaces.
3.Worked examples (2)1:23:59
More worked examples on basis and dimension of vector spaces.
4.Worked examples (3)18:05
More worked examples on basis and dimension of vector spaces.
6Matrix Spaces
Meaning, bases and dimensions of vector spaces derived from matrices - row, column and null spaces.
Chapter lessons
1.Row space20:57
Meaning and illustration of the row space of a matrix.
2.Column space39:26
Meaning and illustration of the column space of a matrix.
3.Null space33:33
Meaning and illustration of the null space of a matrix.
7Sums and Intersections
Sums and intersections of subspaces of a vector space - their basis, dimension and other properties.
Chapter lessons
1.Sums16:53
Meaning of the sum of two subspaces of a vector space.
2.Intersections8:43
Bases and dimensions of the sum and intersection of two subspaces of a vector space.
3.Worked examples (1)1:25:26
Worked examples on bases and dimensions of the sum and intersection of two subspaces of a vector space.
8Coordinates
Meaning of coordinates of a vector in a vector space with respect to a given basis, and how to find the coordinates.
Chapter lessons
1.Definition17:07
Meaning of the coordinates of a vector with respect to a given basis.
2.Worked examples (1)15:54
Worked examples on the coordinates of a vector with respect to a given basis of its vector space.