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 Th23

.= M1 + ((- M2) @) by A1

.= M1 + (- (M2 @)) by Th26

.= M1 - M2 by A2 ;

hence M1 - M2 is symmetric ; :: thesis: verum

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 Th23

.= M1 + ((- M2) @) by A1

.= M1 + (- (M2 @)) by Th26

.= M1 - M2 by A2 ;

hence M1 - M2 is symmetric ; :: thesis: verum