Artificial intelligent assistant

premultiplication

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premultiplication
premultipliˈcation Math. [pre- A. 2.] Multiplication by a prefactor.1862 Phil. Trans. R. Soc. CLI. 316 Let that maxtrix be reduced by premultiplication with a unit-matrix. 1972 Computer Jrnl. XV. 250/2 Pre- and post-multiplication is preserved. Oxford English Dictionary
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Alpha compositing
Alpha Matting and Premultiplication Computer graphics algorithms wikipedia.org
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Proof that inverse of a matrix is unique _If B and C are both inverses of the matrix A,then B=C_. Can't i prove it in following way ? Proof: `AB=BA=I` and `AC=CA=I`,then `BA=CA=I` By postmultiplication $\Rightar...
There is much much simpler. $B=BI=B(AC)=(BA)C=IC=C$
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RGBA color model
It also does not state whether or not the colors are premultiplied by the alpha value, and if they are it does not state what color space that premultiplication wikipedia.org
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If $A,B$ are invertible so $AB$ is invertible I thought about the following proofs but I am not sure about them 1. there is $C,D$ so that $AC=CA=I$ and $BD=DB=I \rightarrow CABD=I \rightarrow$ due to associativity ...
Premultiplication: $B^{-1}A^{-1}AB = B^{-1}(A^{-1}A)B = B^{-1}IB = B^{-1}B = I $ The postmultiplication should be obvious.
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Matrix for rotation around a vector I'm trying to figure out the general form for the matrix (let's say in $\mathbb R^3$ for simplicity) of a rotation of $\theta$ around an arbitrary vector $v$ passing through the ori...
(For those of an advanced bent, one constructs $\mathbf W$ from $\mathbf{\hat u}$ through a premultiplication with the Levi-Civita tensor.)
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unit
▪ I. unit, n. (and a.) (ˈjuːnɪt) Also 6–8 unite. [f. L. ūn-us one; the ending was probably suggested by digit and composit(e. Introduced by Dee, who thus draws attention to the form in his Math. Pref. (1570) *iij marg., Note the worde, Vnit, to expresse the Greke Monas, and not Vnitie: as we haue al... Oxford English Dictionary
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تجميع ألفا
Alpha Matting and Premultiplication خوارزميات رسوميات حاسوبية wikipedia.org
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