There are unknown way to visualize subspace, or vector spaces. You can stretching the width of the x axis, for example, in the right line of a 3d stereo image, and also get depth, as shown below. L R |____| |______| TIP: To get the 3d depth, close one eye and focus on either left or right line, and then open it. This because the z axis uses x to get depth. Which means that you can get double depth to the image.... 4d depth??? :O p.s You're good teacher!
Hello, Prof. Johnston. Really like your linear algebra videos. I also loved your theorem environments. Very pretty. Would it be possible to share a template?
LaTeX source code is now available here: www.njohnston.ca/la_tex.zip If you don't download directly from that link (some browsers don't like external direct links to .zip files), go to njohnston.ca/publications/introduction-to-linear-and-matrix-algebra/ and scroll down to find the course note LaTeX source code.
Yep, when we say that a set "goes through" the origin, we just mean that it contains the origin (i.e., the zero vector). Since R^2 contains the zero vector, R^2 "goes through" the origin.
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Thank you sir! Appreciate the effort👏
thank you so much for these!!!!!
There are unknown way to visualize subspace, or vector spaces.
You can stretching the width of the x axis, for example, in the right line of a 3d stereo image, and also get depth, as shown below.
L R
|____| |______|
TIP: To get the 3d depth, close one eye and focus on either left or right line, and then open it.
This because the z axis uses x to get depth. Which means that you can get double depth to the image.... 4d depth??? :O
p.s
You're good teacher!
Hello, Prof. Johnston. Really like your linear algebra videos.
I also loved your theorem environments. Very pretty. Would it be possible to share a template?
I will once the video series is done and I clean up the TeX code a bit :)
LaTeX source code is now available here: www.njohnston.ca/la_tex.zip
If you don't download directly from that link (some browsers don't like external direct links to .zip files), go to njohnston.ca/publications/introduction-to-linear-and-matrix-algebra/ and scroll down to find the course note LaTeX source code.
But does all of R2 go through origin for it to be called a subspace ?
Yep, when we say that a set "goes through" the origin, we just mean that it contains the origin (i.e., the zero vector). Since R^2 contains the zero vector, R^2 "goes through" the origin.