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Gradient Covariance |
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page 3 of 4 Because I want to use some standard matrix algebra formulas, the above equations can be recast in general form. This introduces the notation
For the
We will later need to express the Then we will use the known formula for inverting 2 x 2 matrices [See also Inverting a Matrix] ![]() Don’t believe me. The first time I did this I made a subtraction error. The way I found there was an error was testing to see if This encapsulates the process of transformations between coordinate systems, which are bidirectional. Using By subtracting the second equation from the first you can obtain The Gradient in the New Coordinate System Our scalar values are expressed as a function F of the
Now by taking partial derivatives we can get the gradient components in the new (barred) coordinate system: Next up: Covariance continued Gradient Covariance page 4 |
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