25 апр. 2013 г. · The Jacobian map is for transforming vectors expressed in terms of one set of coordinate basis vectors into another coordinate system's basis vectors.

10 мая 2021 г. · Jacobian in coordinate transformations when the new coordinates are multifunction's of old ones. · The definition of polar coordinates makes a ...

6 авг. 2017 г. · If we write f(x+iy)=u(x,y)+iv(x,y) where u,v are real, we can compute the Jacobian in the usual way as |uxuyvxvy|=uxvy−uyvx.

6 нояб. 2015 г. · The Jacobian (intuitively) describes how surface (or volume) elements change under a particular coordinate transformation.

22 февр. 2016 г. · The Jacobian describes the local dilation (ie Stretching, compression, etc. at each point) of the coordinate volume element relative to a Cartesian coordinate ...

16 дек. 2019 г. · Consider a transformation between the coordinates given by xa to another system given by coordinates x′a. So a transformation of the type: xa→x′ ...

21 июн. 2017 г. · The term "Jacobian" traditionally refers to the determinant of the derivative matrix. The derivative matrix can be thought of as a local transformation matrix.

20 окт. 2014 г. · The determinant of a unitary matrix is either one or minus one, the absolute value of the determinant of the Jacobian matrix is 1.

22 авг. 2017 г. · The Jacobian of a coordinate transformation may vanish at certain singular points, which have to be excluded from consideration.

11 авг. 2013 г. · The determinant is the product of the lengths of the partial derivatives. The "trick" is that the partial derivatives are orthogonal to each other.