[HN Gopher] Numerical Linear Algebra Class in Julia TUM
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       Numerical Linear Algebra Class in Julia TUM
        
       Author : darboux
       Score  : 134 points
       Date   : 2025-05-03 21:22 UTC (1 days ago)
        
 (HTM) web link (venkovic.github.io)
 (TXT) w3m dump (venkovic.github.io)
        
       | staplung wrote:
       | Not exactly the same material but U. Michigan has their Robotics
       | 101 course up as well: Computational Linear Algebra, also in
       | Julia.
       | 
       | https://github.com/michiganrobotics/rob101/tree/main
        
       | ted_dunning wrote:
       | This is a nicely comprehensive course, but it looks like it is
       | pretty fast paced, especially in the last few lectures (some of
       | those later slides definitely aren't finished).
       | 
       | As a reference, it looks very useful.
        
       | stabbles wrote:
       | A good resource is Gerard Sleijpen's course:
       | https://webspace.science.uu.nl/~sleij101/Opgaven/NumLinAlg/
        
       | me3meme wrote:
       | I just selected lecture 07 to take a look: Lecture 07 is about QR
       | factorizacion and Householder reflections. The author proves how
       | to construct a reflection to make zeros in the first column and
       | then he just claims that following this procedure for the other
       | columns finish the proof. But he should prove or justify why the
       | other reflections do not destroy the zeros of previous
       | reflections. Also he proves that a vector v is the vector to
       | construct the reflection (but there is a factor of 2 that was not
       | correctly simplified, maybe a latex error), but I think that it
       | should be more general and easier to prove that for any w the
       | vector from w to its image f(w) is the orthogonal vector to the
       | plane of the reflection.
       | 
       | I thank the author for the slides, but this little proof need
       | some more care, I don't know about the quality of other sections
       | or the overall quality of the slides. Anyway I like how he tries
       | to make things easy but good work is hard.
       | 
       | Edited: I was wondering whether a LLM reading Lecture 7 would
       | detect what was missing in the proof. I tried with deepseek but
       | its first feedback on the Lecture 7 was positive, then when
       | prompted about the incomplete proof it recognized it as a common
       | error and explained how to complete the proof. Also I have to
       | prompt it about the bad factor 2 for it to detect it. So it seems
       | that deepseek is not a useful tool to judge quality of math
       | content without very expert guidance, deepseek suggested to ask
       | the LLM to compare this proof with another proof to detect
       | important or vital differences.
        
         | Certhas wrote:
         | That's an absolutely obvious step though? As in, detailed
         | lecture notes should maybe elaborate with a sentence, but in a
         | lecture I would not put this on the slides but mention the core
         | point and expect students at this level (who should have seen
         | some amount of more theoretical LinAlg courses by then) to
         | understand how to do the 1 line calculation.
         | 
         | There aren't even any real details to fill in, you iterate on
         | the lower right block so anything you do is orthogonal to the
         | upper left block. Do a 2x2 block matrix multiplication to
         | convince yourself that this preserves the form achieved so far.
        
           | me3meme wrote:
           | -- Do a 2x2 block matrix multiplication to convince yourself
           | that this preserves the form achieved so far.
           | 
           | I don't consider this a proof. Perhaps you have in mind two
           | simple but key properties of reflections about the hyperplane
           | orthogonal to a vector v: (a) The hyperplane of a reflection
           | is the fixed point of the reflection (b) the hyperplane is
           | the orthogonal vector space to the vector space spanned by v.
           | From this two properties it follows that each step of making
           | zeroes does not change previous zeroes.
           | 
           | Your claim that for advanced students there is no need to
           | comment about details it is not falsifiable. Citing Mac Lane:
           | A monad is just a monoid in the category of endofunctors.
           | 
           | But from a practical point of view one can see the very basic
           | level and simplicity of the definitions and calculations
           | prior to the proof. So at this level of detail I consider
           | that noticing that one must be careful to not destroy
           | previous zeros is matching the level of discourse at the
           | proper level.
        
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