Mixing
How do I invert this matrix?
$begingroup$
Given two vectors $$vec{v} = begin{pmatrix}
v_1\
vdots\
v_n
end{pmatrix} ,
vec{w} = begin{pmatrix}
w_1\
vdots\
w_n
end{pmatrix} in mathbb{R}^n$$
such that for all $1 leq j, k leq n$
$v_j neq v_k $ for $j neq k$
$w_j neq w_k $ for $j neq k$
$v_j neq w_k $- $v_j >0 quad $
- $w_j >0 quad $
Define a Matrix $A in mathbb{R^{n times n}}$ with entries $a_{jk}$, for $1 leq j, k leq n$, by
$$a_{j k} :=frac{1}{(v_j - w_k)^2}$$
Is there any simple way to get an expression for its inverse?
I'm really a newbie in linear algebra, this object seems simple enough to be already known, but I can't solve this nor find it solved anywhere.
Thanks in advance! :)
linear-algebra matrices inverse
asked Jan 17 at 14:11
Rocco Rocco
15410
$endgroup$
add a comment |
$begingroup$
Given two vectors $$vec{v} = begin{pmatrix}
v_1\
vdots\
v_n
end{pmatrix} ,
vec{w} = begin{pmatrix}
w_1\
vdots\
w_n
end{pmatrix} in mathbb{R}^n$$
such that for all $1 leq j, k leq n$
$v_j neq v_k $ for $j neq k$
$w_j neq w_k $ for $j neq k$
$v_j neq w_k $- $v_j >0 quad $
- $w_j >0 quad $
Define a Matrix $A in mathbb{R^{n times n}}$ with entries $a_{jk}$, for $1 leq j, k leq n$, by
$$a_{j k} :=frac{1}{(v_j - w_k)^2}$$
Is there any simple way to get an expression for its inverse?
I'm really a newbie in linear algebra, this object seems simple enough to be already known, but I can't solve this nor find it solved anywhere.
Thanks in advance! :)
linear-algebra matrices inverse
asked Jan 17 at 14:11
Rocco Rocco
15410
$endgroup$
add a comment |
$begingroup$
Given two vectors $$vec{v} = begin{pmatrix}
v_1\
vdots\
v_n
end{pmatrix} ,
vec{w} = begin{pmatrix}
w_1\
vdots\
w_n
end{pmatrix} in mathbb{R}^n$$
such that for all $1 leq j, k leq n$
$v_j neq v_k $ for $j neq k$
$w_j neq w_k $ for $j neq k$
$v_j neq w_k $- $v_j >0 quad $
- $w_j >0 quad $
Define a Matrix $A in mathbb{R^{n times n}}$ with entries $a_{jk}$, for $1 leq j, k leq n$, by
$$a_{j k} :=frac{1}{(v_j - w_k)^2}$$
Is there any simple way to get an expression for its inverse?
I'm really a newbie in linear algebra, this object seems simple enough to be already known, but I can't solve this nor find it solved anywhere.
Thanks in advance! :)
linear-algebra matrices inverse
asked Jan 17 at 14:11
Rocco Rocco
15410
$endgroup$
Given two vectors $$vec{v} = begin{pmatrix}
v_1\
vdots\
v_n
end{pmatrix} ,
vec{w} = begin{pmatrix}
w_1\
vdots\
w_n
end{pmatrix} in mathbb{R}^n$$
such that for all $1 leq j, k leq n$
$v_j neq v_k $ for $j neq k$
$w_j neq w_k $ for $j neq k$
$v_j neq w_k $- $v_j >0 quad $
- $w_j >0 quad $
Define a Matrix $A in mathbb{R^{n times n}}$ with entries $a_{jk}$, for $1 leq j, k leq n$, by
$$a_{j k} :=frac{1}{(v_j - w_k)^2}$$
Is there any simple way to get an expression for its inverse?
I'm really a newbie in linear algebra, this object seems simple enough to be already known, but I can't solve this nor find it solved anywhere.
Thanks in advance! :)
linear-algebra matrices inverse
linear-algebra matrices inverse
asked Jan 17 at 14:11
Rocco Rocco
15410
asked Jan 17 at 14:11
Rocco Rocco
15410
edited Jan 17 at 18:01
user635162
asked Jan 17 at 14:11
Rocco Rocco
15410
asked Jan 17 at 14:11
Rocco Rocco
15410
asked Jan 17 at 14:11
Rocco Rocco
15410
15410
add a comment |
add a comment |
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