Linear algebra is concerned with vector spaces of all dimensions and linear transformations between them, including systems of linear equations, bases, dimensions, subspaces, matrices, determinants, traces, eigenvalues and eigenvectors, diagonalization, Jordan forms, etc. For questions specifically ...

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Did I correctly derive the scheme for this PDE using the Crank Nicolson Method?

I'm taking an Applied Numerical Methods course this semester, and I was given the following homework problem: Basically, before I begin writing any sort of code, I would like to ensure that I have ...
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Coefficients of spherical solution to Laplace's equation with difficult Robin boundary conditions

I'm trying to solve Laplace's equation in an (axisymmetric) external spherical domain. The controlling equation is: $$\nabla^2 f = 0$$ $f$ must dissappear at infinity, and at the surface of the ...
3
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3answers
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Vector Addition and Subtraction - interpretation

If we have two vectors $a$ and $b$, both in $\Bbb R^n$, is it correct to think of $a-b$ as how similar the two vectors are? $a + b$ as moving the vector $a$ in the direction of vector $b$?
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Why a form is positive only if its matrix in some ordered basis is a positive matrix?

I'm reading Hoffman's "Linear Algebra" Chapter 9 "Operators on Inner Product Spaces" and got lost at the positive property on (sesqui-linear) forms, operators and matrices. The confusing comes from ...
3
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1answer
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Explicit homotopy equivalence of homogeneous spaces $O(2n)/U(n)$ and $GL(2n,\mathbb{R})/GL(n,\mathbb{C})$

Exercise 2.25 of symplectic topology by McDuff and Salamon asks me to prove that $O(2n)/U(n)$ is homotopy equivalent to $GL(2n,\mathbb{R})/GL(n,\mathbb{C})$. They suggest to use the polar ...