let n be Nat; :: thesis: for K being Field
for M1, M2 being Matrix of n,K st M1 is symmetric & M2 is symmetric holds
M1 + M2 is symmetric
let K be Field; :: thesis: for M1, M2 being Matrix of n,K st M1 is symmetric & M2 is symmetric holds
M1 + M2 is symmetric
let M1, M2 be Matrix of n,K; :: thesis: ( M1 is symmetric & M2 is symmetric implies M1 + M2 is symmetric )
assume that
A1: M1 is symmetric and
A2: M2 is symmetric ; :: thesis: M1 + M2 is symmetric
(M1 + M2) @ = (M1 @) + (M2 @) by Th24
.= M1 + (M2 @) by A1, Def5
.= M1 + M2 by A2, Def5 ;
hence M1 + M2 is symmetric by Def5; :: thesis: verum