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Mintys.Tensor istorija

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2016 birželio 19 d., 12:33 atliko AndriusKulikauskas -
Pakeistos 1-40 eilutės iš
Žr. [[Matematika]]

>>bgcolor=#FFFFC0<<

Šešeriopai suvoktą daugybą (multiplication) suvokti tensoriais (kovariantiškumu, kontravariantiškumu).

>><<

Constructing the most informative illustration of tensors.


Use 2x2 change in coordinates.

Use coordinate system for equilateral triangles and also a coordinate system for squares.


Determine:
* What is the manifold?


Dualities:
* Bottom-up and top-down.
* Tangent vector space and cotangent vector space.

Definition of a tensor:
* ''A tensor of type (p, q) is a map which maps each basis f of vector space V to a multidimensional array T[f] such that if fR is another basis, then T[fR] = ...R-1...R T[f].''
* ''W:VxVx...xVxV*xV*...xV* -> R is a multilinear map (where V* is the dual space of covectors of the space V of vectors).''

Determinant is top-down to define what is "inside" and what is "outside". A shape like the Moebius band is no fun because you can't make that distinction, you can't "understand" it, it does not make a "marked opposite". It is an unmarked duality. But for understanding we want a primitive marked duality, an irreducible marked duality. This is possible through the six transformations of perspectives given by the Holy Spirit.

Negative correlations vs. positive correlations. Yes vs. No.

[[https://forum.azimuthproject.org/discussion/1681/programming-advanced-classical-mechanics-sussman-free-text#latest | Understanding the Lagrangian]]. Consider Kinectic Energy as "bottom-up" approach and Potential Energy as "top-down" approach. Kinetic Energy is finite and Potential Energy is possibly infinite. DT=−D is (roughly) anti-self adjointness.
* Nature maximizes the explicit with regard to the infinite (thus kinectic energy with regard to potential energy). This minimization is related to the avoidance of the collapse of the wave function if at all possible. Nature prefers the complex (unmarked opposites) over the reals (marked opposites). Nature minimizes the marked opposites.

R is super rich but can't handle itself root wise, algebraically. But just a small "shift" is required to add unmarked opposites and have C. Unmarked opposites are "implications" rather than "explications".

Cramer's rule for inverses involves replacing a column in the matrix with the column with the constants. Replacing a column implies a "top down" orthogonal system. Also, the determinant is an anti-symmetric top-down system which distinguishes inside and outside. Whereas the symmetric case does not distinguish inside and outside and leaves them as unmarked opposites. In order to have marked opposites, we need to have a system of anti-symmetry.

Šešeriopai suvoktą dauginimąsi (multiplication) suvokti, išsakyti tensoriais.
į:
Žr. [[Book/Tensor]]
2016 gegužės 30 d., 17:08 atliko AndriusKulikauskas -
Pakeistos 38-40 eilutės iš
Cramer's rule for inverses involves replacing a column in the matrix with the column with the constants. Replacing a column implies a "top down" orthogonal system. Also, the determinant is an anti-symmetric top-down system which distinguishes inside and outside. Whereas the symmetric case does not distinguish inside and outside and leaves them as unmarked opposites. In order to have marked opposites, we need to have a system of anti-symmetry.
į:
Cramer's rule for inverses involves replacing a column in the matrix with the column with the constants. Replacing a column implies a "top down" orthogonal system. Also, the determinant is an anti-symmetric top-down system which distinguishes inside and outside. Whereas the symmetric case does not distinguish inside and outside and leaves them as unmarked opposites. In order to have marked opposites, we need to have a system of anti-symmetry.

Šešeriopai suvoktą dauginimąsi (multiplication) suvokti, išsakyti tensoriais
.
2016 gegužės 26 d., 21:08 atliko AndriusKulikauskas -
Pridėtos 2-7 eilutės:

>>bgcolor=#FFFFC0<<

Šešeriopai suvoktą daugybą (multiplication) suvokti tensoriais (kovariantiškumu, kontravariantiškumu).

>><<
2016 gegužės 22 d., 09:14 atliko AndriusKulikauskas -
2016 gegužės 21 d., 08:04 atliko AndriusKulikauskas -
Pakeista 32 eilutė iš:
Cramer's rule for inverses involves replacing a row and column in the matrix with one from the eigenvector. The eigenvectors are a "top down" orthogonal system. Also, the determinant is an anti-symmetric top-down system which distinguishes inside and outside. Whereas the symmetric case does not distinguish inside and outside and leaves them as unmarked opposites. In order to have marked opposites, we need to have a system of anti-symmetry.
į:
Cramer's rule for inverses involves replacing a column in the matrix with the column with the constants. Replacing a column implies a "top down" orthogonal system. Also, the determinant is an anti-symmetric top-down system which distinguishes inside and outside. Whereas the symmetric case does not distinguish inside and outside and leaves them as unmarked opposites. In order to have marked opposites, we need to have a system of anti-symmetry.
2016 gegužės 20 d., 13:53 atliko AndriusKulikauskas -
Pridėtos 31-32 eilutės:

Cramer's rule for inverses involves replacing a row and column in the matrix with one from the eigenvector. The eigenvectors are a "top down" orthogonal system. Also, the determinant is an anti-symmetric top-down system which distinguishes inside and outside. Whereas the symmetric case does not distinguish inside and outside and leaves them as unmarked opposites. In order to have marked opposites, we need to have a system of anti-symmetry.
2016 gegužės 19 d., 21:22 atliko AndriusKulikauskas -
Pridėtos 29-30 eilutės:

R is super rich but can't handle itself root wise, algebraically. But just a small "shift" is required to add unmarked opposites and have C. Unmarked opposites are "implications" rather than "explications".
2016 gegužės 19 d., 21:07 atliko AndriusKulikauskas -
Pridėta 28 eilutė:
* Nature maximizes the explicit with regard to the infinite (thus kinectic energy with regard to potential energy). This minimization is related to the avoidance of the collapse of the wave function if at all possible. Nature prefers the complex (unmarked opposites) over the reals (marked opposites). Nature minimizes the marked opposites.
2016 gegužės 19 d., 16:21 atliko AndriusKulikauskas -
Pakeista 27 eilutė iš:
[[https://forum.azimuthproject.org/discussion/1681/programming-advanced-classical-mechanics-sussman-free-text#latest | Understanding the Lagrangian]]. Consider Kinectic Energy as "bottom-up" approach and Potential Energy as "top-down" approach. Kinetic Energy is finite and Potential Energy is possibly infinite.
į:
[[https://forum.azimuthproject.org/discussion/1681/programming-advanced-classical-mechanics-sussman-free-text#latest | Understanding the Lagrangian]]. Consider Kinectic Energy as "bottom-up" approach and Potential Energy as "top-down" approach. Kinetic Energy is finite and Potential Energy is possibly infinite. DT=−D is (roughly) anti-self adjointness.
2016 gegužės 19 d., 16:20 atliko AndriusKulikauskas -
Pakeista 27 eilutė iš:
Consider Kinectic Energy as "bottom-up" approach and Potential Energy as "top-down" approach. Kinetic Energy is finite and Potential Energy is possibly infinite.
į:
[[https://forum.azimuthproject.org/discussion/1681/programming-advanced-classical-mechanics-sussman-free-text#latest | Understanding the Lagrangian]]. Consider Kinectic Energy as "bottom-up" approach and Potential Energy as "top-down" approach. Kinetic Energy is finite and Potential Energy is possibly infinite.
2016 gegužės 19 d., 16:14 atliko AndriusKulikauskas -
Pridėtos 26-27 eilutės:

Consider Kinectic Energy as "bottom-up" approach and Potential Energy as "top-down" approach. Kinetic Energy is finite and Potential Energy is possibly infinite.
2016 gegužės 16 d., 16:22 atliko AndriusKulikauskas -
Pridėta 25 eilutė:
Negative correlations vs. positive correlations. Yes vs. No.
2016 gegužės 16 d., 15:58 atliko AndriusKulikauskas -
Pridėtos 22-23 eilutės:

Determinant is top-down to define what is "inside" and what is "outside". A shape like the Moebius band is no fun because you can't make that distinction, you can't "understand" it, it does not make a "marked opposite". It is an unmarked duality. But for understanding we want a primitive marked duality, an irreducible marked duality. This is possible through the six transformations of perspectives given by the Holy Spirit.
2016 gegužės 02 d., 21:45 atliko AndriusKulikauskas -
Pridėta 21 eilutė:
* ''W:VxVx...xVxV*xV*...xV* -> R is a multilinear map (where V* is the dual space of covectors of the space V of vectors).''
2016 gegužės 02 d., 21:42 atliko AndriusKulikauskas -
Pakeista 20 eilutė iš:
*
į:
* ''A tensor of type (p, q) is a map which maps each basis f of vector space V to a multidimensional array T[f] such that if fR is another basis, then T[fR] = ...R-1...R T[f].''
2016 gegužės 02 d., 21:34 atliko AndriusKulikauskas -
Pridėtos 1-21 eilutės:
Žr. [[Matematika]]

Constructing the most informative illustration of tensors.


Use 2x2 change in coordinates.

Use coordinate system for equilateral triangles and also a coordinate system for squares.


Determine:
* What is the manifold?


Dualities:
* Bottom-up and top-down.
* Tangent vector space and cotangent vector space.

Definition of a tensor:
*

Tensor


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Puslapis paskutinį kartą pakeistas 2016 birželio 19 d., 12:33