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Jul
27
revised The rows of an orthogonal matrix form an orthonormal basis
mainly, removing the basis tag (see meta http://meta.math.stackexchange.com/q/21091), other small fixes
Jul
27
revised Reading a basis for $\operatorname{Null}(A)$ and $\operatorname{Null}(A^T)$ from the reduced row-echelon form of $A$
fixing stuff left over
Jul
27
revised Why people use the Gram-Schmidt process instead of just chosing the standard basis
Mainly, removing the (basis) tag; see meta http://meta.math.stackexchange.com/q/21091
Jul
27
revised Finding a matrix representation of the linear transformation $T\colon P_2\to P_2$ ($T(f) = f''+2f'-f$)
added 52 characters in body; edited tags; edited title
Jul
27
revised Is it possible to partition a basis $S$ of a Euclidean vector space into a basis for a subspace $U$ and its orthogonal complement?
mainly, removing the(basis) tag. See meta http://meta.math.stackexchange.com/q/2109
Jul
27
comment Why the transformation matrix is composed by the transformation of the vector in the basis?
Note that $L$ is not a linear transformation, since $L( \begin{bmatrix}0 & 0 \end{bmatrix}^T ) = \begin{bmatrix} 1 & 0 \end{bmatrix}^T$. (Linear transformations send the zero vector to the zero vector.) Also, the standard (ordered) basis plays an important role in determining the matrix of a linear transformation, when that ordered basis is used.
Jul
27
revised Why the transformation matrix is composed by the transformation of the vector in the basis?
added 7 characters in body; edited tags
Jul
27
revised Check for basis of a matrix
deleted 25 characters in body; edited tags
Jul
27
revised Basis of the intersection of two spans
added 7 characters in body; edited tags
Jul
27
revised Strength of the statement “$\mathbb R$ has a Hamel basis over $\mathbb Q$”
added 43 characters in body; edited tags; edited title
Jul
27
revised Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$?
mainly, removed (basis) tag
Jul
27
revised Should I use set notation or list notation when writing out a basis of vectors?
deleted 14 characters in body; edited tags; edited title
Jul
26
revised Are the coordinate functions of a Hamel basis for an infinite dimensional Banach space discontinuous?
deleted 13 characters in body; edited tags
Jul
25
revised Locally connected Locally compact separable metric space
included other answer as an edit. MathJaxed.
Jul
24
comment Supportive book(s) for unproven-theorems of General Topology by R Engelking?
Yeah, I think those examples are perfect exercises. For 3.7.1 the only real obstacle to show that the map is perfect is showing that it is closed, which the (fully proven) Kuratowski theorem gives you; there is no reason to re-prove this. For 3.7.16 since $\beta Y$ is a compactification of $Y$, if something holds for all compactifications of $Y$, it holds for $\beta Y$. Similarly, if something holds for $\beta Y$, it holds for some compactification of $Y$. If these implications are not obvious, maybe you don't have the "mathematical maturity" to handle Engelking at this point.
Jul
24
comment Supportive book(s) for unproven-theorems of General Topology by R Engelking?
Can you give an example (or examples) of the kind of unproven theorems in Engelking you are talking about?
Jul
24
comment Ordering $2n$ numbers
So are you asking for, given $n$, the number of sequences $a_0,a_1,a_2,...,a_{2n-1},a_{2n}=a_0$ where (1) $a_0,...,a_{2n-1}$ list each of $1,...,2n$, (2) $a_i < a_{i+1}$ for even $i < 2n$, and (3) $a_i > a_{i+1}$ for odd $i < 2n$? (For example, if $n=2$ then $2,3,1,4,2$ is legal, but $3,4,1,2,3$ is not.)
Jul
23
revised Suppose every convergent Sequence has a unique limit point in space $X$, then $X$ is Hausdorff
Minor correction; some improvement
Jul
23
comment Looking for this theorem by Devlin and Shelah
Have you tried searching MathSciNet? According to the Shelah archive, Devlin has been a co-author with Shelah on only four papers.
Jul
23
revised How do I solve this deceleration problem?
rolled back to a previous revision