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Let $A$ be $n\times n$. $A$ is left invertiable if there exists some $n\times n$ matrix $B$ such that $BA=I_n$, where $B$ is the left inverse.
$A$ is right invertaible if there exists some $n\times n$ matrix $C$ such that $AC=I_n$, where $C$ is the right inverse.
If both the left and right inverse exists, then $A$ is invertible if there exists some $B$ such that $AB=I_n=BA$. We usually denote the inverse with $A^{-1}$ such that $A^{-1}A=AA^{-1}=I$.
$A$ is right invertaible if there exists some $n\times n$ matrix $C$ such that $AC=I_n$, where $C$ is the right inverse.
If both the left and right inverse exists, then $A$ is invertible if there exists some $B$ such that $AB=I_n=BA$. We usually denote the inverse with $A^{-1}$ such that $A^{-1}A=AA^{-1}=I$.
Concepts
For finite square matrices, if $A$ is left invertible then it is also right invertible. However if $A$ is an infinite square matrix, then it may only have a left or right inverse.Inverses can be conputed with block matrices. Form an augmnted matrix $[A|I_n]$, then row reduce until the left hand side is in row reduced echelon form and we get $[R|P]$. Then $A$ is invertible if and only if $R=I_n$ and $P=A^{-1}$
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Let $A$ be $n\times n$. $A$ is left invertiable if there exists some $n\times n$ matrix $B$ such that $BA=I_n$, where $B$ is the left inverse.
$A$ is right invertaible if there exists some $n\times n$ matrix $C$ such that $AC=I_n$, where $C$ is the right inverse.
If both the left and right inverse exists, then $A$ is invertible if there exists some $B$ such that $AB=I_n=BA$. We usually denote the inverse with $A^{-1}$ such that $A^{-1}A=AA^{-1}=I$.
$A$ is right invertaible if there exists some $n\times n$ matrix $C$ such that $AC=I_n$, where $C$ is the right inverse.
If both the left and right inverse exists, then $A$ is invertible if there exists some $B$ such that $AB=I_n=BA$. We usually denote the inverse with $A^{-1}$ such that $A^{-1}A=AA^{-1}=I$.
Concepts
For finite square matrices, if $A$ is left invertible then it is also right invertible. However if $A$ is an infinite square matrix, then it may only have a left or right inverse.Inverses can be conputed with block matrices. Form an augmnted matrix $[A|I_n]$, then row reduce until the left hand side is in row reduced echelon form and we get $[R|P]$. Then $A$ is invertible if and only if $R=I_n$ and $P=A^{-1}$
Used In
Coming soonHypothesis
Coming soonResults
Coming soon
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