Dec
9
awarded  Caucus
Nov
22
comment How to determine the smallest interpolation degree required?
Use progressive interpolation. When the degree is reached, the new points to interpolate will already be interpolated.
Oct
18
revised How to build a orthogonal basis from a vector?
some sign errors
Oct
15
comment Orthogonal Vectors in a 2D Lattice with minimum area
Minimizing a determinant interestingly enough is the same as lattice reduction, at least for two by two. I believe that is the case anyway from my memories of past musings... Think in terms of orthogonalizing the two vectors (so basically swap two elements of one vector, determinant becomes dot product of the two vectors)
Oct
15
comment Orthogonal Vectors in a 2D Lattice with minimum area
Now I see though that $i$ or $k$ zero is the same thing which you did note.
Oct
15
comment Orthogonal Vectors in a 2D Lattice with minimum area
My thought is that only $A$ and $B$ need be linearly dependent (or $B$ and $C$) in order to find orthogonal vectors.
Oct
15
comment Orthogonal Vectors in a 2D Lattice with minimum area
For this problem, one need not look only at the Gram matrix since the orthogonal vectors need not be in the same basis, only in the same lattice. I would guess that you have such a habit of using the Gram matrix from looking at binary quadratic forms.
Oct
14
comment Non square inversion
a pseudoinverse would work. In this case where there is an exact solution, you could also look at each column separately. Column 1 gives two equations,$0=0$ and $0.5 k_{x1} = -1$
Oct
12
answered Mathematical expression to form a vector from diagonal elements
Sep
30
awarded  Yearling
Sep
30
awarded  Explainer
Aug
12
revised Determinant of block matrices with non square matrices
edited body
Jul
28
answered Method of orthogonalization that preserves invertibility
Jul
28
comment Method of orthogonalization that preserves invertibility
Also, you would have to work on columns of one and rows of the other. Is that what you mean by acting the same either way?
Jul
28
comment Method of orthogonalization that preserves invertibility
I imagine just about any matrix is a counter example, and any method that chooses one vector from the matrix to keep and orthogonalize the other vectors with will not do what you ask. Because choosing a vector from the inverse in a similar manner will definitely not coincide with any choice in the main matrix (unless of course that vector is already orthogonal from all others). I would say no such method exists unless it calculates and works with the inverse as well.
Jul
2
awarded  Curious
Jul
1
awarded  Necromancer
May
16
comment What are some good iPhone/iPod Touch/iPad Apps for mathematicians?
looks like the for iOS link is gone.
Apr
3
accepted $\Delta^d m^n =d! \sum_{k} \left[ m \atop k \right] { {k+n} \brace m + d}(-1)^{m+k}$ Is this a new formula?
Mar
29
comment $\Delta^d m^n =d! \sum_{k} \left[ m \atop k \right] { {k+n} \brace m + d}(-1)^{m+k}$ Is this a new formula?
I have posted more details on the MO Question