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 Apr16 revised Evaluating norm of the operator corrected notation error (x_n instead of z_n) Apr16 revised Find multivariable limit $\frac{x^2y}{x^2+y^3}$ Replaced a wrong solution with a correct one. Apr16 answered Find multivariable limit $\frac{x^2y}{x^2+y^3}$ Mar25 answered show invariant subspace is direct sum decomposition Mar25 reviewed Approve Is Linear Algebra the foundation of Applied Mathematics? Mar19 revised Proving that given any two points in a connected manifold, there exists a diffeomorphism taking one to the other added 20 characters in body Mar19 answered Proving that given any two points in a connected manifold, there exists a diffeomorphism taking one to the other Mar1 awarded Revival Dec20 awarded Constituent Dec20 answered What are some interesting sole exceptions or counterexamples? Dec10 awarded Caucus Nov24 comment Confusing Analysis proof Because you represent a bilinear form $f \colon V \otimes V \rightarrow \mathbb{F}$ and not a linear map $L \colon V \rightarrow V$. You can read about it in any reference that discusses bilinear forms - for example, people.virginia.edu/~mah7cd/Math5651/Lecture15.pdf. Nov23 revised Confusing Analysis proof Addressed an additional question Nov23 comment Confusing Analysis proof I'll add an explanation in an hour or so, but the point is that a bilinear form doesn't have a well-defined notion of a determinant as a number, only the ratio makes sense, and you can compute it any way you want. Nov23 comment How to show existence of an orthogonal map? Hint: Complete $\frac{x}{||x||}$ to an orthonormal basis $(e_1, \ldots, e_n)$, complete $\frac{y}{||y||}$ to an orthonormal basis $(f_1, \ldots, f_n)$ and define $T$ by describing how it acts on $e_i$. Nov23 answered Confusing Analysis proof Nov17 revised Adaptions I have to make to go from integer coefficients to coefficients in $R$ edited tags Sep30 awarded Explainer Sep6 comment Can there exist a non diagonal matrix whose inverse is diagonal matrix? Yes, it is like in a field with respect to addition or multiplication or like in a vector space with respect to addition. Sep2 answered Kernel of linear transformation composition