Tnx alot Dr. Hower I'M MS. Student at Computer Science minor Datamining. Your teaching in so useful funny and I'm not bored never ever to study your teaching I hope you will record more and more lecture for us Ahmad
@@DrValerieHower Yeah and I love how unique you are as a person and I love your tattoos I'm so honoured you took your time I'll ace linear algebra in 2021 thanks to you❣❣😇🎓I also want to be a professor one day
In this example I am discussing orthogonal complement. if V is the span of a collection of vectors. and we want a basis for the orthogonal complement of V, we can put those vectors as rows of a matrix M and find a basis for ker(M). that is what I discuss here.
I believe you are asking about the example when I have V is the span of 2 linearly independent vectors in R^3. The orthogonal complement will be a 3-2=1 dimensional subspace of R^3. I am not sure where your reference to R^4 is coming from. Thank you.
Thank you for this lesson. Quick question: for the example finding "orthonormal complement", the first one for instance, couldn't we just "solve for kernel" and put [1 3 1 -1] as a column, so it becomes 4x1 matrix waiting to be reduced? but I guess it's not making sense yet...
Hi. If you have a 4x1 nonzero matrix (meaning 4 rows and 1 column), this will be a rank 1 matrix. Its kernel will be the 0 subspace sitting inside the real line. To find the orthogonal complement of the span of (1,3,1,-1), we would put this vector as a ROW and solve for the kernel of that matrix. I believe this is what I discuss towards the end of this video. thank you.
@@DrValerieHower Got it, thank you - I was aware of putting this vector(s) as a Row, but I didn't understand it yet. By definition, 'orthogonal complement' is Ker(T), and I recall previously when solving for kernel, the basis vectors were put into Columns instead. Here also, I'm thinking the span of one single vector is a line in the space. That said, too many things covered and I couldn't get it all yet!
@sndme by definition, the orthogonal complement of a subspace is the set of all vectors perpendicular to every vector in the subspace. Here are my current notes on this section (a bit different than the video) if this helps: drive.google.com/file/d/1mVAWCDhH7KydN5RLkUKz7F1VcpqSA9nH/view?usp=sharing
Thank you for your question. In the current syllabus, we do not cover chapter 4 at Northeastern. So, I do not have videos on it. Some professors may teach it here if they have time in the schedule, but I have not yet had time for this chapter.
Thank you for posting this, helps with my college linear algebra class in terms of actually understanding the material.
You are welcome. Thank you so much for the feedback!!
Tnx alot Dr. Hower
I'M MS. Student at Computer Science minor Datamining.
Your teaching in so useful funny and I'm not bored never ever to study your teaching
I hope you will record more and more lecture for us
Ahmad
thank you so much for your feedback :)
You are such a brilliant teacher I'm so glad and lucky I found you
Thank you so much!
@@DrValerieHower Yeah and I love how unique you are as a person and I love your tattoos I'm so honoured you took your time I'll ace linear algebra in 2021 thanks to you❣❣😇🎓I also want to be a professor one day
thank you ma'am .... finally my doubts cleared 😀😀
You are welcome! Thanks for the feedback.
Thanks, mam for this fascinating lecture!
You are welcome and thank you for your feedback.
Thank you Dr.. I really enjoyed the lecture
You are very welcome. I appreciate the feedback
Do you mind posting your notes packets as well in the description? Love to get some extra practice!
Thanks a lot Mam!
You are welcome. I appreciate the comment.
Hi at 59:11. Why are we writing the matrix with rows as opposed to columns like we usually do?
In this example I am discussing orthogonal complement. if V is the span of a collection of vectors. and we want a basis for the orthogonal complement of V, we can put those vectors as rows of a matrix M and find a basis for ker(M). that is what I discuss here.
In the last question, where we find a basis for the orthogonal complement, why do we need a vector in R3 pls? I thought it would go from R4 to R4?
I believe you are asking about the example when I have V is the span of 2 linearly independent vectors in R^3. The orthogonal complement will be a 3-2=1 dimensional subspace of R^3. I am not sure where your reference to R^4 is coming from. Thank you.
Thank you for this lesson. Quick question: for the example finding "orthonormal complement", the first one for instance, couldn't we just "solve for kernel" and put [1 3 1 -1] as a column, so it becomes 4x1 matrix waiting to be reduced? but I guess it's not making sense yet...
Hi. If you have a 4x1 nonzero matrix (meaning 4 rows and 1 column), this will be a rank 1 matrix. Its kernel will be the 0 subspace sitting inside the real line. To find the orthogonal complement of the span of (1,3,1,-1), we would put this vector as a ROW and solve for the kernel of that matrix. I believe this is what I discuss towards the end of this video. thank you.
@@DrValerieHower Got it, thank you - I was aware of putting this vector(s) as a Row, but I didn't understand it yet. By definition, 'orthogonal complement' is Ker(T), and I recall previously when solving for kernel, the basis vectors were put into Columns instead. Here also, I'm thinking the span of one single vector is a line in the space. That said, too many things covered and I couldn't get it all yet!
@sndme by definition, the orthogonal complement of a subspace is the set of all vectors perpendicular to every vector in the subspace. Here are my current notes on this section (a bit different than the video) if this helps: drive.google.com/file/d/1mVAWCDhH7KydN5RLkUKz7F1VcpqSA9nH/view?usp=sharing
Which of your videos is sect 4.1linear spaces in the book?
Thank you for your question. In the current syllabus, we do not cover chapter 4 at Northeastern. So, I do not have videos on it. Some professors may teach it here if they have time in the schedule, but I have not yet had time for this chapter.