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From a theoretical perspective the most fundamental decomposition is the rank-decomposition: A = X D Y with X,Y invertible and D diagonal. It's called rank decomposition, because you can read off the rank from A by counting the non-zero entries in D. It's also useful to determining bases for the image and the kernel of A. Every math student learns a version of that in their first lecture series of Linear Algebra. Cur…
This “rank decomposition” is a bit interesting algebraically rather than numerically, since then the numerical stability problems disappear. Also, if we take all matrices to be over the integers (and require that “invertible” means the inverse is also an integer matrix), then the rank decomposition is a lot like the Smith normal form of a matrix.
Any suggestions on what to learn in Linear Algebra after Gilbert Strang’s 18.06SC? https://ocw.mit.edu/courses/18-06sc-linear-algebra-fall-2011... My goal is to learn the math behind machine learning.
From a theoretical perspective the most fundamental decomposition is the rank-decomposition: A = X D Y with X,Y invertible and D diagonal. It's called rank decomposition, because you can read off the rank from A by counting the non-zero entries in D. It's also useful to determining bases for the image and the kernel of A. Every math student learns a version of that in their first lecture series of Linear Algebra. Cur…
Any suggestions on what to learn in Linear Algebra after Gilbert Strang’s 18.06SC? https://ocw.mit.edu/courses/18-06sc-linear-algebra-fall-2011... My goal is to learn the math behind machine learning.
https://ocw.mit.edu/courses/18-065-matrix-methods-in-data-an...
Any suggestions on what to learn in Linear Algebra after Gilbert Strang’s 18.06SC? https://ocw.mit.edu/courses/18-06sc-linear-algebra-fall-2011... My goal is to learn the math behind machine learning.
Thank you for this wonderfully concise summary: it’s convenient to have all this in one compact document. I suppose “flops” means “floating-point operations” here? Heretofore I’ve always encountered this as an abbreviation for “floating-point operations per second”.
Any suggestions on what to learn in Linear Algebra after Gilbert Strang’s 18.06SC? https://ocw.mit.edu/courses/18-06sc-linear-algebra-fall-2011... My goal is to learn the math behind machine learning.
You could take Strang’s follow-up course on learning from data. https://ocw.mit.edu/courses/18-065-matrix-methods-in-data-an...
Thank you for this wonderfully concise summary: it’s convenient to have all this in one compact document. I suppose “flops” means “floating-point operations” here? Heretofore I’ve always encountered this as an abbreviation for “floating-point operations per second”.
It's always been very ambiguous in practice. To avoid ambiguity I usually use `flop/s` but not everyone likes that :)
Flop/s makes no sense and is outright wrong. The whole point of flops is to express how many floating point operations are required by an algorithm. How many operations are performed per second is a property of the hardware you're using to run an implementation of the algorithm.
You want to express computational complexity in terms of floating point operations.