Ziyad Hossain’s Reviews > Linear Algebra Done Right > Status Update
Ziyad Hossain
is on page 95 of 251
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
— Oct 28, 2026 09:31PM
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
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Ziyad’s Previous Updates
Ziyad Hossain
is on page 160 of 251
Eigenvalues and Eigenvectors talk about matrices that have a scalar relationship to some arbitrary vector. I don’t like this anymore
— Nov 03, 2026 11:48AM
Ziyad Hossain
is on page 30 of 251
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.
— Oct 07, 2026 11:58AM
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.