Following the lecture - Githubissues

mandli / intro-numerical-methods

Jupyter notebooks and other materials developed for the Columbia course APMA 4300

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Following the lecture #37

Closed vincentqb closed 7 years ago

vincentqb commented 7 years ago

I mostly changed the align environment to $$ that I couldn't parse for the presentation.

Two more things:

Line 72 with the <,> was also causing some problems, so I replaced by \langle and \rangle.
Also, this sentence was not clear to me: "Another way to write this is that $x_k$ is orthogonal to all the rest of the vectors in the set $X$." and I was understanding it as: "Another way to write this is that any $x_k$ has a component orthogonal to all the rest of the vectors in the set $X$." Is that what you meant?

mandli commented 7 years ago

@vincentqb What system were you running this on and what version of Jupyter? I am surprised that the aligns did not work.

mandli commented 7 years ago

Also, for the orthogonality, the precise statement should be $\forall v \in X, <x_k, v> = 0$ except when $v = x_k$. Does that better represent the statement?

vincentqb commented 7 years ago

The align environment does not render on the github page either.

I'm on Ubuntu 16.04. Jupyter notebook's about: The version of the notebook server is 4.2.3 and is running on: Python 3.5.2 |Anaconda 2.5.0 (64-bit)| (default, Jul 2 2016, 17:53:06) [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)] Python 3.5.2 |Anaconda 2.5.0 (64-bit)| (default, Jul 2 2016, 17:53:06) IPython 5.1.0 -- An enhanced Interactive Python.

mandli commented 7 years ago

Huh, the version of Jupyter and IPython are the same. The only big difference is the version of Python (I usually use 2.7 still). Seems odd that it would have regressed though. Does the following fix the rendering?

https://github.com/jupyter/nbviewer/issues/590

vincentqb commented 7 years ago

X is a list of vectors, not necessarily forming a linear space, right? I understand x_k to be a generic linear combination of vectors in X that may or may not be in X. Is that correct? For example, if I take x_k as (1,0) but X={(0,1),(1,1)} then x_k is a linear combination of vectors in X, but x_k is not orthogonal to the vectors in X. Did I get x_k and X right?

mandli commented 7 years ago

X is a set of linearly independent vectors. From the wording I see how this could be confusing though as x_k \in X but in the cell above is written as a contradiction of the statement.

mandli commented 7 years ago

I changed some of the aligns and fixed the angled brackets in commit e3a0bca5b5c2d53a16a122eea5c20a08b1387adc