Dear Dr. Valerie Hower, thank you so much for sharing these Linear Algebra tutorials. The explanations are clear with meaningful examples. Your tutorials are super helpful! I have learned a lot from them. Much appreciated! :D
I love the linear combination point of view. Also we can view matrix multiplication A_n,m * x, as a transformation from the row space of A_n,m which is equivalent to R^m (since the number of columns is the length of a row vector) , to the column space of the matrix R^n (since the number of rows is the length of a column vector).
Hello Dr. Valerie Hower, sorry I have one question : what is the text you are refering to for the course I can't find any info in the description, thank you in advance.
Thank you for your videos. They are really good. As a comment, you define linear transformation with matrices and then state its properties as a Theorem, but because it can extend to infinite dimensional spaces, it is better to first defined with the properties and then one proves the relation with matrices. Am I right?
Hi. Thanks for the comment. You are correct that your approach extends. I was following the textbook used at Northeastern University which defines a linear transformation in terms of a matrix first. But the more abstract approach (with properties first) is a good one.
I believe your question is about matrix of a transformation. Generally if T has domain R^m, we evaluate T(e1), T(e2), ... T(em) and put these vectors as columns in matrix A. e1, e2, .... em are the standard vectors in R^m. (1,0,0,0) is e1 in R^4. I hope this answers your question. Thank you!
Dear Dr. Valerie Hower, thank you so much for sharing these Linear Algebra tutorials. The explanations are clear with meaningful examples. Your tutorials are super helpful! I have learned a lot from them. Much appreciated! :D
You are welcome. Thank you so much for your feedback!
Can I just say, how easy you make this look! THANK YOU!
You are so welcome! I appreciate the feedback :)
Thank you so much professor I'm struggling without linear algebra started it late last month hope to finish this month
Genia doctora, saludos desde Argentina
You are so awesome pedagogue. ❤ your pedagogy
Life saver
I love the linear combination point of view. Also we can view matrix multiplication A_n,m * x, as a transformation from the row space of A_n,m which is equivalent to R^m (since the number of columns is the length of a row vector) , to the column space of the matrix R^n (since the number of rows is the length of a column vector).
Hi. you make an excellent observation. However, we must be careful. The row space need not be all of R^m.
It is 2am. My exam is at 1:40pm. I'm praying this lecture will save. Ive been trying so hard to understand.
Best wishes on your exam!
literally very energetic lecture
Thank you!!
Tysm. That was really helpful ❤️
That's wonderful to hear. You are welcome!
Thank you!
You're welcome!
Thanks teacher ❤
You are welcome!!
Hello Dr. Valerie Hower, sorry I have one question : what is the text you are refering to for the course I can't find any info in the description, thank you in advance.
I use the book "Linear Algebra with Applications" 5th Edition by Otto Bretscher.
Thank you for your videos. They are really good. As a comment, you define linear transformation with matrices and then state its properties as a Theorem, but because it can extend to infinite dimensional spaces, it is better to first defined with the properties and then one proves the relation with matrices. Am I right?
Hi. Thanks for the comment. You are correct that your approach extends. I was following the textbook used at Northeastern University which defines a linear transformation in terms of a matrix first. But the more abstract approach (with properties first) is a good one.
In 33:09 how to get those 1000 for T,I don’t get it?
I believe your question is about matrix of a transformation. Generally if T has domain R^m, we evaluate T(e1), T(e2), ... T(em) and put these vectors as columns in matrix A. e1, e2, .... em are the standard vectors in R^m. (1,0,0,0) is e1 in R^4. I hope this answers your question. Thank you!