2 ms·

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 sli

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 1y ago
-- 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.
- Certhas 1y ago
  10 LB = LB' 0Q 0A 0A' The proof says iterate on A, so that obviously creates a lower dimensional rotation Q that will act on the full space as above. Absolutely mention this in lecture notes/during the lecture.

me3meme 1y ago

-- 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.

Certhas 1y ago
10 LB = LB' 0Q 0A 0A' The proof says iterate on A, so that obviously creates a lower dimensional rotation Q that will act on the full space as above. Absolutely mention this in lecture notes/during the lecture.