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The early History of the Singular Value Decomposition (1993) [pdf]

math.ucdavis.edu

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Re: The early History of the Singular Value Decomposition (1993) [pdf]

#81

Post by waynecochran »

bee_rider wrote: post #80
waynecochran wrote: post #78

Earlier quoted context omitted.

Here is an example. I wrote a MacOS app in Objective-C++/C++ that used Eigen's JacobiSVD solver at one point. A colleague of mine use Claude to port it into a web tool that used JavaScript. I scrolled thru the JS code and saw that is wrote is own Jacobi SVD solver. So I assume it did this match the exact behavior of the MacOS app -- using a 3rd party solver may not accomplish this. SVD solvers can behave differently…

Not sure, I’m not familiar with the web ecosystem. Not familiar at all, so my next question will probably be stupid. Would it have been possible to compile your C++ library to WebAssembly?

I am sure it probably was - a bit heavier option. There other mobile / VR / XR apps that I had to port to a variety of platforms using languages like Swift and Kotlin -- each platform has its own vector library. These don't necessarily provide SVD routines. Apple has their Accelerate framework, but is very unnatural to use IMO -- and Swift and C++ don't play that well together regardless of what folks say (that is why I tend to still use Obj-C++ when I have a choice).

There was another app where I had a 3x3 shear transformation that I needed to decompose into a rotation * scale * rotation which is exactly what SVD does (see https://tinyurl.com/384mkdvh). No need to bring in a full linear algebra package just for that.

Re: The early History of the Singular Value Decomposition (1993) [pdf]

#82

Post by srean »

jacobolus wrote: post #79
srean wrote: post #73

Earlier quoted context omitted.

I have mixed feelings about this. BTW my comment is not about Axler's linear algebra book but math pedagogy in general. Spoon feeding doesn't really help with learning, internalising, building internalisation for. Effort and frustration is key. For me the best way has been to be forced to discover the important properties and results myself. It is slow but effective and best for knowledge retention. I think the best…

The big problem I have with Axler's presentation of the SVD is that it's backwards. It leads with a bunch of completely dry and technical minutiae written formally, loads students up with tedious and confusing technical exercises they aren't likely to appreciate, and defers the motivation, context, explanation, and pictures until a few dozen pages later (probably multiple weeks later for a course), and in my opinion…

I mostly agree.

I wouldn't have liked Axler as my first book of linear algebra but as a second book, it worked, it gave me a more algebraic appreciation which is a bit against my natural grain of vector space and geometric way of thinking.

I quite liked Linear Algebra Done Wrong. My first linear algebra book was Noble's.

Re: The early History of the Singular Value Decomposition (1993) [pdf]

#83

Post by shusaku »

waynecochran wrote: post #76
shusaku wrote: post #56

Earlier quoted context omitted.

Claude is absolutely terrible at writing unit tests, this advice continues to perplex me. Coding agents usually slam you with hundreds of lines that do little more than “test” what is obvious. Maybe it’s good for an API revision or such. But for linear algebra where errors might not manifest unless suitably chosen inputs are generated based on expert knowledge, that’ll be useless.

Have you used Claude lately? It definitely will outperform a human at this task now.

I use it literally every day. But please do not use it to generate tests on its own, it’s all sleight of hand. It does not (without substantial guidance and tweaking from an expert) have the capability to generate meaningful tests.

Re: The early History of the Singular Value Decomposition (1993) [pdf]

#84

Post by aptitude_moo »

fooblaster wrote: post #75
aptitude_moo wrote: post #39

Earlier quoted context omitted.

I'm not the person you are replying to but I work in image processing of SAR radar images and it's mostly ML-free (thankfully because I don't enjoy it). I dont know which other areas still work with these things

What sort of algorithms do you run on SAR images?

For example, to create the image from the radar pulses, you can do time-domain backprojection, omega-k and others. Then when comparing images of different dates you can do SAR interferometry, then use numerical methods, iterative algorithms. Although I'm thinking this may be called signal processing instead of computer vision.

Re: The early History of the Singular Value Decomposition (1993) [pdf]

#85

Post by toolslive »

wtallis wrote: post #6
toolslive wrote: post #4

Earlier quoted context omitted.

Just going to sound really pedantic here, but RGB does not capture the entire colour space. In fact, it only captures about 35% of the colours the human eye can perceive. https://www.oceanopticsbook.info/view/photometry-and-visibil...

You seem to be conflating "RGB" with one particular RGB color space: sRGB. That's a common enough conflation to make, but not appropriate when you're trying to be pedantic.

hold on. Just realised it's not even (part of ) a vector space. It's not linear, non-euclidian and can't be mapped onto 3 dimensions. It's not even constant or always reproducible:

    Look at an object; 
    Observe colour X; then look at the wrong thing; 
    then look back and you might observe colour X' != X.
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