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The name of an $n\times n$ matrix with positive real elements satisfying $a_{ij}=1/a_{ji}$ for all $i,j\in\{1,2,\ldots n\}$ is reciprocal matrix.
A consistent reciprocal matrix has elements of the form $a_{ij}=w_i/w_j$, so that $a_{ij}a_{jk}=a_{ik}$. Its largest eigenvalue is equal to $n$ (here is a proof)
Consistent reciprocal matrices have applications in decision theory.

The name of an $n\times n$ matrix with positive real elements satisfying $a_{ij}=1/a_{ji}$ for all $i,j\in\{1,2,\ldots n\}$ is reciprocal matrix.
A consistent reciprocal matrix has elements of the form $a_{ij}=w_i/w_j$, so that $a_{ij}a_{jk}=a_{ik}$. Its largest eigenvalue is equal to $n$ (here is a proof)
Consistent reciprocal matrices have applications in decision theory.

The name of an $n\times n$ matrix with positive real elements satisfying $a_{ij}=1/a_{ji}$ is reciprocal matrix. A consistent reciprocal matrix has elements of the form $a_{ij}=w_i/w_j$, so that $a_{ij}a_{jk}=a_{ik}$. Then its largest eigenvalue is equal to $n$ (here is a proof)
Consistent reciprocal matrices have applications in decision theory.

The name of an $n\times n$ matrix with positive real elements satisfying $a_{ij}=1/a_{ji}$ for all $i,j\in\{1,2,\ldots n\}$ is reciprocal matrix.
A consistent reciprocal matrix has elements of the form $a_{ij}=w_i/w_j$, so that $a_{ij}a_{jk}=a_{ik}$. Its largest eigenvalue is equal to $n$ (here is a proof)
Consistent reciprocal matrices have applications in decision theory.

The name of an $n\times n$ matrix with positive real elements satisfying $a_{ij}=1/a_{ji}$ is reciprocal matrix, with the "consistency property" that if its largest eigenvalue $λ_{max}$ is equal to $n$, then $a_{ij}a_{jk}=a_{ik}$ where $i,j,k\in\{1,2,...,n\}$.

The name of an $n\times n$ matrix with positive real elements satisfying $a_{ij}=1/a_{ji}$ is reciprocal matrix. A consistent reciprocal matrix has elements of the form $a_{ij}=w_i/w_j$, so that $a_{ij}a_{jk}=a_{ik}$. Then its largest eigenvalue is equal to $n$ (here is a proof)
Consistent reciprocal matrices have applications in decision theory.