Rank of linear transformation $T(P)=QP$ where $Q$ has rank $2$
$begingroup$
Suppose $ Q in M_{3}(mathbb R)$ is the matrix of rank $2$. Let $T:M_{3}(mathbb R)to M_{3}(mathbb R)$ be the linear transformation defined by $T(P)=QP$. Then find rank of linear transformation.
Rank of $Q$ is $2$ does it mean that $Q$ have $2$ pivot when reduce by echelon from or it means that it has $2$ distinct elements which form part of basis ?
As $dim(mathrm{range}(T))+dim(mathrm{null}(T))=9$ and since $PQ$ is the product it can have rank atmost $2$ does it mean rank of linear transformation is less than or equal to $2$ ?
linear-algebra matrices linear-transformations
asked Dec 26 '18 at 15:35
sejysejy
1589
$endgroup$
add a comment |
$begingroup$
Suppose $ Q in M_{3}(mathbb R)$ is the matrix of rank $2$. Let $T:M_{3}(mathbb R)to M_{3}(mathbb R)$ be the linear transformation defined by $T(P)=QP$. Then find rank of linear transformation.
Rank of $Q$ is $2$ does it mean that $Q$ have $2$ pivot when reduce by echelon from or it means that it has $2$ distinct elements which form part of basis ?
As $dim(mathrm{range}(T))+dim(mathrm{null}(T))=9$ and since $PQ$ is the product it can have rank atmost $2$ does it mean rank of linear transformation is less than or equal to $2$ ?
linear-algebra matrices linear-transformations
asked Dec 26 '18 at 15:35
sejysejy
1589
$endgroup$
1
$begingroup$
See this question.
$endgroup$
– Dietrich Burde
Dec 26 '18 at 16:04
add a comment |
$begingroup$
Suppose $ Q in M_{3}(mathbb R)$ is the matrix of rank $2$. Let $T:M_{3}(mathbb R)to M_{3}(mathbb R)$ be the linear transformation defined by $T(P)=QP$. Then find rank of linear transformation.
Rank of $Q$ is $2$ does it mean that $Q$ have $2$ pivot when reduce by echelon from or it means that it has $2$ distinct elements which form part of basis ?
As $dim(mathrm{range}(T))+dim(mathrm{null}(T))=9$ and since $PQ$ is the product it can have rank atmost $2$ does it mean rank of linear transformation is less than or equal to $2$ ?
linear-algebra matrices linear-transformations
asked Dec 26 '18 at 15:35
sejysejy
1589
$endgroup$
Suppose $ Q in M_{3}(mathbb R)$ is the matrix of rank $2$. Let $T:M_{3}(mathbb R)to M_{3}(mathbb R)$ be the linear transformation defined by $T(P)=QP$. Then find rank of linear transformation.
Rank of $Q$ is $2$ does it mean that $Q$ have $2$ pivot when reduce by echelon from or it means that it has $2$ distinct elements which form part of basis ?
As $dim(mathrm{range}(T))+dim(mathrm{null}(T))=9$ and since $PQ$ is the product it can have rank atmost $2$ does it mean rank of linear transformation is less than or equal to $2$ ?
linear-algebra matrices linear-transformations
linear-algebra matrices linear-transformations
asked Dec 26 '18 at 15:35
sejysejy
1589
asked Dec 26 '18 at 15:35
sejysejy
1589
edited Dec 26 '18 at 18:01
sejy
asked Dec 26 '18 at 15:35
sejysejy
1589
asked Dec 26 '18 at 15:35
sejysejy
1589
asked Dec 26 '18 at 15:35
sejysejy
1589
1589
1
$begingroup$
See this question.
$endgroup$
– Dietrich Burde
Dec 26 '18 at 16:04
add a comment |
1
$begingroup$
See this question.
$endgroup$
– Dietrich Burde
Dec 26 '18 at 16:04
1
1
$begingroup$
See this question.
$endgroup$
– Dietrich Burde
Dec 26 '18 at 16:04
$begingroup$
See this question.
$endgroup$
– Dietrich Burde
Dec 26 '18 at 16:04
add a comment |
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$begingroup$
See this question.
$endgroup$
– Dietrich Burde
Dec 26 '18 at 16:04