- #1
Dassinia
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Hello this is not a homework, just studying for the exam, and :
Consider E a linear space with dot product (.,.) and the norm ||x|| = sqrt(x,x)
a and b two orthogonals elements of E
Find the value of ||a+ b|| et||a- b|| and ||a+ b||-||a- b||
a and b orthogonals means that ||a||=||b||=1
||a+b||=√(a+b,a+b) = √[(a,a)+(b,a)+(a,b)+(b,b) ] =√[ 1+0+0+1 ] = √2
||a-b||=√(a-b,a-b) = √[(a,a)+(-b,a)+(a,-b)+(-b,-b) ] =√[ 1-(b,a)+(-b,a)*-1 ] = √[ 1-(b,a)-(b,a)*-1 ]=0
||a+b||-||a-b||=√2
Is that correct ?
Homework Statement
Consider E a linear space with dot product (.,.) and the norm ||x|| = sqrt(x,x)
a and b two orthogonals elements of E
Find the value of ||a+ b|| et||a- b|| and ||a+ b||-||a- b||
Homework Equations
The Attempt at a Solution
a and b orthogonals means that ||a||=||b||=1
||a+b||=√(a+b,a+b) = √[(a,a)+(b,a)+(a,b)+(b,b) ] =√[ 1+0+0+1 ] = √2
||a-b||=√(a-b,a-b) = √[(a,a)+(-b,a)+(a,-b)+(-b,-b) ] =√[ 1-(b,a)+(-b,a)*-1 ] = √[ 1-(b,a)-(b,a)*-1 ]=0
||a+b||-||a-b||=√2
Is that correct ?