Translation for "bilineaarinen" to english

Bilineaarinen

• bilinear

Translation examples

bilinear

Monimutkaisiin laskelmiin perustuva Bibubic-interpolointimenetelmä tuottaa tasaisempia liukusävyjä kuin bilineaarinen tai lähimmän naapurin menetelmä.
Using complex calculations, Bicubic produces smoother tonal gradations than the Bilinear or Nearest Neighbor resampling methods.

Kun kerroinkuntana ovat kompleksiluvut, kahden vektorin sisätulo on yleensä kompleksiluku, ja sisätulo on seskvilineaarinen, ei bilineaarinen.
The inner product of two vectors over the field of complex numbers is, in general, a complex number, and is sesquilinear instead of bilinear.

Pistetuloa luonnehtii näin ollen geometrisesti A ⋅ B = A B ‖ B ‖ = B A ‖ A ‖ . {\displaystyle \mathbf {A} \cdot \mathbf {B} =A_{B}\left\|\mathbf {B} \right\|=B_{A}\left\|\mathbf {A} \right\|.} Tähän tapaan määriteltynä pistetulo on homogeeninen skaalattaessa jokaista muuttujaa, mikä merkitsee, että jokaiselle skalaarille α {\displaystyle \alpha } pätee: ( α A ) ⋅ B = α ( A ⋅ B ) = A ⋅ ( α B ) . {\displaystyle (\alpha \mathbf {A} )\cdot \mathbf {B} =\alpha (\mathbf {A} \cdot \mathbf {B} )=\mathbf {A} \cdot (\alpha \mathbf {B} ).} Pistetulolle pätee myös osittelulaki, toisin sanoen A ⋅ ( B + C ) = A ⋅ B + A ⋅ C . {\displaystyle \mathbf {A} \cdot (\mathbf {B} +\mathbf {C} )=\mathbf {A} \cdot \mathbf {B} +\mathbf {A} \cdot \mathbf {C} .} Näistä ominaisuuksista yhteen­vetona voidaan todeta, että pistetulo on bilineaarinen muoto.
The dot product is thus characterized geometrically by a ⋅ b = a b ‖ b ‖ = b a ‖ a ‖ . {\displaystyle \mathbf {a} \cdot \mathbf {b} =a_{b}\left\|\mathbf {b} \right\|=b_{a}\left\|\mathbf {a} \right\|.} The dot product, defined in this manner, is homogeneous under scaling in each variable, meaning that for any scalar α, ( α a ) ⋅ b = α ( a ⋅ b ) = a ⋅ ( α b ) . {\displaystyle (\alpha \mathbf {a} )\cdot \mathbf {b} =\alpha (\mathbf {a} \cdot \mathbf {b} )=\mathbf {a} \cdot (\alpha \mathbf {b} ).} It also satisfies a distributive law, meaning that a ⋅ ( b + c ) = a ⋅ b + a ⋅ c . {\displaystyle \mathbf {a} \cdot (\mathbf {b} +\mathbf {c} )=\mathbf {a} \cdot \mathbf {b} +\mathbf {a} \cdot \mathbf {c} .} These properties may be summarized by saying that the dot product is a bilinear form.