Qt front-end for FluidSynth.
One of the defining properties of algebraic structure with two operations such as ring and field:This property shows how the two operations interact.
We define this as the functional equation:It is a bit like cauchy's functional equation but with multiplication instead of addition.
Existence and uniqueness results are fundamental in mathematics because we often define objects by their properties, and then start calling them "the object", which is fantastically convenient.
But calling something "the object" only makes sense if there exists exactly one, and only one, object that satisfies the properties.
One particular context where these come up very explicitly is in solutions to differential equations, e.g. existence and uniqueness of solutions of partial differential equations.
Same remarks as Section "Exam".
Has been going wild with restoration and reverse engineering of the Apollo moon mission.
Inside the WILD Lab of CuriousMarc by Keysight Labs (2022)
Source. - youtu.be/qwocVH3_1Eo?t=841 the IBM System/360 is insane!
TODO what is the point of them? Why not just sum over every index that appears twice, regardless of where it is, as mentioned at: www.maths.cam.ac.uk/postgrad/part-iii/files/misc/index-notation.pdf.
Those in indices on bottom are called contravariant vectors.
It is possible to change between them by Raising and lowering indices.
The values are different only when the metric signature matrix is different from the identity matrix.
Applications of eigenvalues and eigenvectors by
Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01
- math.stackexchange.com/questions/23312/what-is-the-importance-of-eigenvalues-eigenvectors/3503875#3503875
- math.stackexchange.com/questions/1520832/real-life-examples-for-eigenvalues-eigenvectors
- matheducators.stackexchange.com/questions/520/what-is-a-good-motivation-showcase-for-a-student-for-the-study-of-eigenvalues
Eigenvectors and eigenvalues of the identity matrix by
Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01
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