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Results tagged with linear-algebra
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user 23862
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
1
vote
1
answer
159
views
Matrix of powers of pairwise differences
Let $\underline{c}:=\left(c_1,\dots,c_n\right)$ be pairwise distinct complex numbers, and let $k$ be a non-negative integer. Define the matrix $A_{n,k}(\underline{c})$ to contain the $k$-th powers of …
- 959
13
votes
2
answers
1k
views
Determinant of $V^* V$ where $V$ is rectangular Vandermonde matrix with nodes on unit circle
Let $z_{1},\dots,z_{k}$
be distinct complex numbers with $\left|z_{j}\right|=1,\;j=1,\dots,k$. For any natural $N\geqslant k$
consider the rectangular Vandermonde matrix
$$
V_{N}=\begin{pmatrix}1 …
- 959
2
votes
Accepted
Norm of inverse confluent Vandermonde matrix
For $j=1,\dots,n$ and $k=0,1,\dots,l_j-1$ denote by $u_{j,k}$ the row with index $l_1+\dots +l_{j-1}+k$ of the matrix $V^{-1}$. By using a generalization of the Hermite interpolation formula (see [3]) …
- 959
8
votes
1
answer
1k
views
Norm of inverse confluent Vandermonde matrix
Let $\{x_1,\dots,x_n\}$ be pairwise distinct complex numbers and $l_1+l_2+\dots+l_n=N$. The $N\times N$ confluent Vandermonde matrix is defined as
$$V=
\begin{bmatrix}
v_{1,0}&v_{2,0}&\dots&v_{n,0}\\\ …
- 959