let K be Field; :: thesis: for n being Nat
for M1, M2 being Matrix of n,K st M1 is symmetric & M2 is symmetric holds
M1 - M2 is symmetric
let n be Nat; :: 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
.= M1 + (- (M2 @)) by Th27
.= M1 - M2 by A2 ;
hence M1 - M2 is symmetric ; :: thesis: verum