Vector field proof
Not what you're looking for?
Please solve attached part b.
Suppose that x<-->A(x) is a smooth mapping from a neighborhood U of R^n containing 0 into the SO(n) matrices, defined by the relations....Show that for any vector field X on U.....
Purchase this Solution
Solution Summary
This provides an example of completing a proof regarding a vector field and a smooth mapping.
Solution Preview
In terms of the entries, matrix multiplication is given by
Important note: here and in what follows I am using the Einstein summation convention, in which we sum over all possible values of any repeated indices . So the right hand side of the above is really shorthand for the sum
Since transposing just involves interchanging rows and columns, we see that
Combining these two facts, we get:
Everything so far has been ...
Purchase this Solution
Free BrainMass Quizzes
Probability Quiz
Some questions on probability
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.