let n be Element of NAT ; :: thesis: for x being FinSequence of REAL
for A being Matrix of n, REAL st n > 0 & len x = n holds
x * (A @ ) = A * x
let x be FinSequence of REAL ; :: thesis: for A being Matrix of n, REAL st n > 0 & len x = n holds
x * (A @ ) = A * x
let A be Matrix of n, REAL ; :: thesis: ( n > 0 & len x = n implies x * (A @ ) = A * x )
assume A1: ( n > 0 & len x = n ) ; :: thesis: x * (A @ ) = A * x
( len A = n & width A = n ) by MATRIX_1:25;
hence x * (A @ ) = A * x by A1, MATRIXR1:53; :: thesis: verum