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Let $A$ be an invertible $n \times n$ matrix and denote by $r_i(A,j)$ the vector with entries as in row $i$ of $A$ with columns from $1,...,j$. We can obtain $r_i(A,j)$ in Sage as follows:

def givesubmatrix(A,i,j):
B=A[[i-1],[0..j-1]]
return(B)

I want to find the permutation $p(M)$ of the set $[ 1,...,n ]$ (it seems set brackets dont work in this forum using latex? So I use [ and ] instead for the set brackets) defined by the condition: $p(A,i):=\min [ j \mid r_i(A,j) \text{ is not in the span of } [{r_i(A,j),...,r_{i-1}(A,j)] } ].$ Is there an easy way to obtain this permutation?

I have already problems to define the subspace $[{r_i(A,j),...,r_{i-1}(A,j)] }$.

Let $A$ be an invertible $n \times n$ matrix and denote by $r_i(A,j)$ the vector with entries as in row $i$ of $A$ with columns from $1,...,j$. We can obtain $r_i(A,j)$ in Sage as follows:

def givesubmatrix(A,i,j):
B=A[[i-1],[0..j-1]]
return(B)

I want to find the permutation $p(M)$ $p(A)$ of the set $[ 1,...,n ]$ (it seems set brackets dont work in this forum using latex? So I use [ and ] instead for the set brackets) defined by the condition: condition:

$p(A,i):=\min [ j \mid r_i(A,j) \text{ is not in the span of } [{r_i(A,j),...,r_{i-1}(A,j)] } ].$ Is there an easy way to obtain this permutation?

I have already problems to define the subspace $[{r_i(A,j),...,r_{i-1}(A,j)] }$.

Let $A$ be an invertible $n \times n$ matrix and denote by $r_i(A,j)$ the vector with entries as in row $i$ of $A$ with columns from $1,...,j$. We can obtain $r_i(A,j)$ in Sage as follows:

def givesubmatrix(A,i,j):
B=A[[i-1],[0..j-1]]
return(B)

I want to find the permutation $p(A)$ of the set $[ 1,...,n ]$ (it seems set brackets dont work in this forum using latex? So I use [ and ] instead for the set brackets) defined by the condition:

$p(A,i):=\min [ j \mid r_i(A,j) \text{ is not in the span of } [{r_i(A,j),...,r_{i-1}(A,j)] } ].$ ].$

Is there an easy way to obtain this permutation?

I have already problems to define the subspace $[{r_i(A,j),...,r_{i-1}(A,j)] }$.}$ using Sage.

Let $A$ be an invertible $n \times n$ matrix and denote by $r_i(A,j)$ the vector with entries as in row $i$ of $A$ with columns from $1,...,j$. We can obtain $r_i(A,j)$ in Sage as follows:

def givesubmatrix(A,i,j):
B=A[[i-1],[0..j-1]]
return(B)

I want to find the permutation $p(A)$ of the set $[ 1,...,n ]$ (it seems set brackets dont work in this forum using latex? So I use [ and ] instead for the set brackets) defined by the condition:

$p(A,i):=\min [ j \mid r_i(A,j) \text{ is not in the span of } [{r_i(A,j),...,r_{i-1}(A,j)] [{r_1(A,j),...,r_{i-1}(A,j)] } ].$

Is there an easy way to obtain this permutation?

I have already problems to define the subspace $[{r_i(A,j),...,r_{i-1}(A,j)] }$ using Sage.

Let $A$ be an invertible $n \times n$ matrix and denote by $r_i(A,j)$ the vector with entries as in row $i$ of $A$ with columns from $1,...,j$. We can obtain $r_i(A,j)$ in Sage as follows:

def givesubmatrix(A,i,j):
 B=A[[i-1],[0..j-1]]
 return(B)

I want to find the permutation $p(A)$ of the set $[ 1,...,n ]$ (it seems set brackets dont work in this forum using latex? So I use [ and ] instead for the set brackets) defined by the condition:

$p(A,i):=\min [ j \mid r_i(A,j) \text{ is not in the span of } [{r_1(A,j),...,r_{i-1}(A,j)] } ].$

Is there an easy way to obtain this permutation?

I have already problems to define the subspace $[{r_i(A,j),...,r_{i-1}(A,j)] }$ using Sage.

Let $A$ be an invertible $n \times n$ matrix and denote by $r_i(A,j)$ the vector with entries as in row $i$ of $A$ with columns from $1,...,j$. We can obtain $r_i(A,j)$ in Sage as follows:

def givesubmatrix(A,i,j):
    B=A[[i-1],[0..j-1]]
    return(B)

I want to find the permutation $p(A)$ of the set $[ $\{ 1,...,n ]$ \} $ (it seems set brackets dont work in this forum using latex? So I use [ and ] instead for the set brackets) defined by the condition:

$p(A,i):=\min [ \{ j \mid r_i(A,j) \text{ is not in the span of } [{r_1(A,j),...,r_{i-1}(A,j)] } ].$\{ {r_1(A,j),...,r_{i-1}(A,j) }} \}.$

Is there an easy way to obtain this permutation?

I have already problems to define the subspace $[{r_i(A,j),...,r_{i-1}(A,j)] }$ using Sage.

Let $A$ be an invertible $n \times n$ matrix and denote by $r_i(A,j)$ the vector with entries as in row $i$ of $A$ with columns from $1,...,j$. We can obtain $r_i(A,j)$ in Sage as follows:

def givesubmatrix(A,i,j):
    B=A[[i-1],[0..j-1]]
    return(B)

I want to find the permutation $p(A)$ of the set $\{ 1,...,n \}$ (it seems set brackets dont work in this forum using latex? So I use [ and ] instead for the set brackets) defined by the condition:

$p(A,i):=\min \{ j \mid r_i(A,j) \text{ is not in the span of } \{ [ {r_1(A,j),...,r_{i-1}(A,j) }} ] \}.$

Is there an easy way to obtain this permutation?

I have already problems to define the subspace $[{r_i(A,j),...,r_{i-1}(A,j)] }$ using Sage.

Let $A$ be an invertible $n \times n$ matrix and denote by $r_i(A,j)$ the vector with entries as in row $i$ of $A$ with columns from $1,...,j$. We can obtain $r_i(A,j)$ in Sage as follows:

def givesubmatrix(A,i,j):
    B=A[[i-1],[0..j-1]]
    return(B)

I want to find the permutation $p(A)$ of the set $\{ 1,...,n \}$ (it seems set brackets dont work in this forum using latex? So I use [ and ] instead for the set brackets) defined by the condition:

$p(A,i):=\min \{ j \mid r_i(A,j) \text{ is not in the span of } [ {r_1(A,j),...,r_{i-1}(A,j) ] \{r_1(A,j),...,r_{i-1}(A,j) \} \}.$

Is there an easy way to obtain this permutation?

I have already problems to define the subspace $[{r_i(A,j),...,r_{i-1}(A,j)] }$ using Sage.

Let $A$ be an invertible $n \times n$ matrix and denote by $r_i(A,j)$ the vector with entries as in row $i$ of $A$ with columns from $1,...,j$. We can obtain $r_i(A,j)$ in Sage as follows:

def givesubmatrix(A,i,j):
    B=A[[i-1],[0..j-1]]
    return(B)

I want to find the permutation $p(A)$ of the set $\{ 1,...,n \}$ (it seems set brackets dont work in this forum using latex? So I use [ and ] instead for the set brackets) defined by the condition:

$p(A,i):=\min \{ j \mid r_i(A,j) \text{ is not in the span of } [ \{r_1(A,j),...,r_{i-1}(A,j) \} \}.$

Is there an easy way to obtain this permutation?

I have already problems to define the subspace generated by $[{r_i(A,j),...,r_{i-1}(A,j)] }$ $\{r_i(A,j),...,r_{i-1}(A,j) \}$ using Sage.