 Eric W. Weisstein conjectured , and McKay et al . ( 2004 ) proved , that the same numbers count the ( 0 @,@ 1 ) matrices for which all eigenvalues are positive real numbers . The proof is bijective : a matrix A is an adjacency matrix of a DAG if and only if A + I is a ( 0 @,@ 1 ) matrix with all eigenvalues positive , where I denotes the identity matrix . Because a DAG cannot have self @-@ loops , its adjacency matrix must have a zero diagonal , so adding I preserves the property that all matrix coefficients are 0 or 1 . 
 Eric W. Weisstein conjectured , and McKay et al . ( 2004 ) proved , that the same numbers count the ( 0 @,@ 1 ) matrices for which all eigenvalues <a href='drop_aux' title='1'><mark>are</mark></a>positive real numbers . The proof <a href='drop_aux' title='2'><mark>is</mark></a>bijective : a matrix A <a href='drop_aux' title='3'><mark>is</mark></a>an adjacency matrix of a DAG if and only if A + I <a href='drop_aux' title='4'><mark>is</mark></a>a ( 0 @,@ 1 ) matrix with all eigenvalues positive , where I <a href='uninflect' title='5'><mark>denotes</mark></a> the identity matrix . Because a DAG cannot have self @-@ loops , its adjacency matrix must have a zero diagonal , so adding I <a href='uninflect' title='6'><mark>preserves</mark></a> the property that all matrix coefficients are 0 or 1 . 
Eric W. Weisstein conjectured , and McKay et al . ( 2004 ) proved , dat the same numbers count da ( 0 @,@ 1 ) matrices for which alll eigenvalues positive real numbers . Tdaproof bijective : a matrix A an adjacency matrix of a DAG if and only if A + I a ( 0 @,@ 1 ) matrix withallll eigenvalues positive , where I denote thdadentity matrix . Because a DAG cannot have self @-@ loops , its adjacency matrix must have a zero diagonal , soo adding I preserve thedaoperty thaalllll matrix coefficients are 0 or 1 .