The linear algebra content is divided into weekly content to provide a pacing for a semester class
Week -1 : Resources
Here are a link to all the other notes which may be of use to you in your study of linear algebra
- A reference to all symbols necessary for the notes Linear Algebra Symbols Here is an explanation of how linear algebra is taught incorrectly:
- They introduce the concepts of systems of linear equations without the proper structure of Vector Spaces. In order to grasp the true concept, one should introduce vector spaces first, then examine polynomials, however polynomials are “concrete/applicable”, that is why it is introduced first
Week 0: Important Definitions
Week 1 : Intro to Polynomials and Systems of Equations
Lecture 1 : Systems Of Equations
Week 2: Vector Spaces and Vector Subspaces
Lecture 4: Vector Space Lecture 5: Vector Sub-Space Lecture 6: Sums and Direct Sums
Week 3: Linear Combinations, Spanning Sets and Linear Independence
Lecture 7: Linear Combinations
Groups, Rings, Fields, VectorSpaces
Random question
If we use the notion of set theory, and we have a vector space V, then a set S that is a subset of V, then what would happen if S was empty?
- Note, if we construct linear algebra without set theory, we don’t care
- Anyways, span could mean either a vector space of only the zero vector, or a vector space of the vector space of the zero-vector with just gives us a vector space with only the zero-vector.but does this mean that an empty set is equivalent to the vector space only containing the zero-vector?