In minute 15:00 you should have written the product as you said and not the quotient between the norm of A and the norm of its inverse. In fact usually one takes this as a definition with a general norm and then one can find other characterizations of the condition number like the one you said between the quotient of the biggest and the smallest eigenvalue
great video. I have an unusually problem I can actually choose A, any guidance how I find the best possible A? assume A is real valued. What if A contains counts, that is to say integers >= 0
***** Lambda min and max are the minimum and maximum eigenvalues in absolute value, indeed. This can be extended to non-symmetric matrices by looking at the singular value instead of the eigenvalues, in the case in which the matrix norm we're considering is induced by the Euclidian norm (note that the condition number depends on which matrix norm you choose). unreal epsilon and lambda are just errors, not the vectors+errors. If the error is small but the original vectors are even smaller, then it's bad. If the error is big but the original vectors are bigger than the error, then it does not matter too much. That's why the scaling matters; it's not the same thing to have an error of 1 when the result is 0.0001 compared to when the result is 10000. +Jeffrey Adams you got the condition number wrong at 15:00
Cheers Jeffrey. You saved me from some quite abstract reading - this went much more painless.
In minute 15:00 you should have written the product as you said and not the quotient between the norm of A and the norm of its inverse. In fact usually one takes this as a definition with a general norm and then one can find other characterizations of the condition number like the one you said between the quotient of the biggest and the smallest eigenvalue
Last part about how to find norm for a non-symmetric matrix is precious!
at about 6:00, should be ||b||=|lambda_i| ||x||
Jep
That made my day. Absolutely fantastic explanation!
Wonderful explanation! Thank you very much!
Awesome videos, helps me a lot, thank you!
At 6.25. isn't ||b|| = |eigenvalue| ||x|| instead of the other way?
yeah ur right
Fantastic explanation! Not the usual beating around the bush..
At minute 6:00 you wrote the wrong equality but still wrote the right one underneath it
best explanation ever!
thank you
One can tell you know this inside out, amazing didactics, too!!
how did you calculate for x and y so easy at 2:00
Thank you!!! Such a good explanation
can we apply norm in calculation of conditional no of a real matrix..
great video. I have an unusually problem I can actually choose A, any guidance how I find the best possible A? assume A is real valued. What if A contains counts, that is to say integers >= 0
Nice video but you wrote one formula wrong. At 15:09 cond(A)=norm(A)*norm(Ainv)
finally I get to know what is well-conditions
Simulation 💻📱
why is it bad if epsilon and delta are scaled? does something matter besides their proportionality?
** What is lambda?????
***** Lambda min and max are the minimum and maximum eigenvalues in absolute value, indeed.
This can be extended to non-symmetric matrices by looking at the singular value instead of the eigenvalues, in the case in which the matrix norm we're considering is induced by the Euclidian norm (note that the condition number depends on which matrix norm you choose).
unreal epsilon and lambda are just errors, not the vectors+errors. If the error is small but the original vectors are even smaller, then it's bad. If the error is big but the original vectors are bigger than the error, then it does not matter too much. That's why the scaling matters; it's not the same thing to have an error of 1 when the result is 0.0001 compared to when the result is 10000.
+Jeffrey Adams you got the condition number wrong at 15:00
Thanks a lot!!!