Timeline for Change of basis in Mathematica
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Dec 27, 2018 at 15:59 | comment | added | jhndoe2 | Let us continue this discussion in chat. | |
| Dec 27, 2018 at 15:54 | comment | added | Henrik Schumacher | The basis change matrix W -> V should be the inverse of the basis change matrix V -> W. | |
| Dec 27, 2018 at 15:40 | comment | added | jhndoe2 | Okay, I'll try to be more clear. English is not my primarylanguage so forgive me for any misunderstandings. First, with your help, I decided the change of basis matrix from the bases V -> W, and after that I verified it so that it'd be correct. Now, I'm trying to decide the change of basis matrix from W -> V instead. | |
| Dec 27, 2018 at 15:08 | comment | added | Henrik Schumacher |
Hmm. It is not entirely clear to me what you look for. If you are looking for a matrix A such that A.W == V, then A = V.Inverse[W] is what you want (just multiply the equation with Inverse[W] from the right). If you seek B such that B.V == W, then B = W.Inverse[V].
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| Dec 27, 2018 at 14:16 | comment | added | jhndoe2 | Well, I'd like to know the change of basis matrix from the base W -> V, so how would the function look like? | |
| Dec 27, 2018 at 14:04 | comment | added | Henrik Schumacher |
You're welcome. I'd rather use V.Inverse[W] or W.Inverse[V] depending on which direction you would like to have.
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| Dec 27, 2018 at 13:51 | comment | added | jhndoe2 | Ah, now I get it. Thank you so much. If i were to calculate the change of basis matrix from W -> V, using the Inverse function, would I first take the inverse of W, and then multiply W^1 * V? | |
| Dec 27, 2018 at 13:36 | history | edited | Henrik Schumacher | CC BY-SA 4.0 |
deleted 2 characters in body
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| Dec 27, 2018 at 13:36 | comment | added | Henrik Schumacher |
ArrayFlatten can merge block matrices to a single matrix. And A[[All, 3 ;;]] reads off the columns 3 to Dimensions[A][[2]] of a matrix A. See the documentation of Part and Span for details.
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| Dec 27, 2018 at 13:34 | comment | added | jhndoe2 | Ah, smart. Wasn't thinking about how you could compare the two functions that easily. Just one question though. What does the ArrayFlatten, and the [[All, 3 ;;]] commands mean? Thank you very much for your answer. | |
| Dec 27, 2018 at 13:32 | history | answered | Henrik Schumacher | CC BY-SA 4.0 |