Support this course by joining Wrath of Math to access exclusive and early linear algebra videos, plus lecture notes at the premium tier! th-cam.com/channels/yEKvaxi8mt9FMc62MHcliw.htmljoin Linear Algebra course: th-cam.com/play/PLztBpqftvzxWT5z53AxSqkSaWDhAeToDG.html Linear Algebra exercises: th-cam.com/play/PLztBpqftvzxVmiiFW7KtPwBpnHNkTVeJc.html
Isomorphisms on vector spaces are actually only defined over the same field, so to say two vector spaces are isomorphic immediately implies they are over the same field.
@@WrathofMathif they had different fields, would it be legitimate to temporarily give them the same field to show their structure is identical, and then change the field back once the proof is done?
Support this course by joining Wrath of Math to access exclusive and early linear algebra videos, plus lecture notes at the premium tier! th-cam.com/channels/yEKvaxi8mt9FMc62MHcliw.htmljoin
Linear Algebra course: th-cam.com/play/PLztBpqftvzxWT5z53AxSqkSaWDhAeToDG.html
Linear Algebra exercises: th-cam.com/play/PLztBpqftvzxVmiiFW7KtPwBpnHNkTVeJc.html
Thank you sir for your very clear and detailed explanations on this subject😊❤
Glad to help - thanks for watching!
9:00 what if V and W have different base fields? How does T translate scalars?
Isomorphisms on vector spaces are actually only defined over the same field, so to say two vector spaces are isomorphic immediately implies they are over the same field.
@@WrathofMathif they had different fields, would it be legitimate to temporarily give them the same field to show their structure is identical, and then change the field back once the proof is done?