Linear Algebra Finite Dimensional Vectors
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All vector spaces are finite dimensional
1) Let X be a finite dimensional linear space. Show that, for every subspace Y of X, Y perp perp = Y (that is, the annihilator of the annihilator of Y is Y)
2) X = U = V = polynomials in s, T=d/ds, S=multiplication by s
Show that S and T are linear and ST is not equal to TS
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Solution Summary
The expert examines finite dimensional linear space. Annihilator of the annihilator is analyzed.
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[1]
In what follows, ^ stands for perp.
Since X is finite dimensional,
X = Y (+) Y^ (direct sum);
in particular, Y / Y^ = {0}
consequently, Y^ / Y^^ = ...
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