Status Updates From Linear Algebra Done Right (...

Eigenvalues and Eigenvectors talk about matrices that have a scalar relationship to some arbitrary vector. I don’t like this anymore

A basis is a representation of the set of all vectors that are linearly independent with one another. In other words the basis can be used to span an entire space. If you have two vectors (1,0) and (0,1) you essentially reach anywhere in R^2.

The dimension of a space is literally what it means but for a matrix it’s the amount of unique paths you can take. So R^2 has dim(A)=2

R and C represent the set of Real numbers and Complex numbers R is a subset of C meaning every real number exists in the Complex world.

You can generalize that to F which is just a field over many dimensions so R^2 means 2D but generalizing this F^N would be either R or C in N dimensions.

A vector space is a space of vectors. Vector spaces have the properties of scalar multiplication and normal addition.

did you know 1+1=0

Learnt about quotient spaces, Product of vector spaces. Very interesting

Learnt about inverses, isomorphism, change of bases etc

Studied about Matrices as linear maps

Reading about Linear maps, null spaces, range etc. And the proofs are really beautiful