Uploaded August 2016 | Updated September 2026, 2 weeks ago
In this video, I briefly describe the concept of linear vector spaces. This is part of my Quantum Mechanics lectures series, and will help you understand some of the mathematics we'll be doing later on.
Questions? Let me know in the comments!
Prereqs: Basic Linear Algebra (at the first year college level) helps but is not absolutely necessary (I think).
Lecture Notes: drive.google.com/file/d/0B_urJu4cgDhMYUstVmpnV3JNME0/view?usp=sharing&resourcekey=0-L-2IVw-TbUjfO1CSKoTLnw
Patreon Link: patreon.com/user?u=4354534
EDIT TO CLARIFY: Instead of "For each phi_i there is a vector 0 such that ..." it should be "There is a vector 0 such that for each phi_i ...". Similarly, for the scalar multiplication, "there is a 1 and a 0 such that for every vector psi ...". I don't want you guys to think that the '1' and the '0' vectors are different for each psi; they are the same for the entire vector space! Also, when I say that a vector space is a set of vectors psi_1, psi_2, psi_3 ..., I don't mean that it's countable. I'm just using psi_1, psi_2, and psi_3 as some example vectors.
In this video, I briefly describe the concept of linear vector spaces. This is part of my Quantum Mechanics lectures series, and will help you understand some of the mathematics we'll be doing later on.
Questions? Let me know in the comments!
Prereqs: Basic Linear Algebra (at the first year college level) helps but is not absolutely necessary (I think).
Lecture Notes: drive.google.com/file/d/0B_urJu4cgDhMYUstVmpnV3JNME0/view?usp=sharing&resourcekey=0-L-2IVw-TbUjfO1CSKoTLnw
Patreon Link: patreon.com/user?u=4354534
EDIT TO CLARIFY: Instead of "For each phi_i there is a vector 0 such that ..." it should be "There is a vector 0 such that for each phi_i ...". Similarly, for the scalar multiplication, "there is a 1 and a 0 such that for every vector psi ...". I don't want you guys to think that the '1' and the '0' vectors are different for each psi; they are the same for the entire vector space! Also, when I say that a vector space is a set of vectors psi_1, psi_2, psi_3 ..., I don't mean that it's countable. I'm just using psi_1, psi_2, and psi_3 as some example vectors.
