I guess it's because u dot v should be equal to v dot u, so the things not on the diagonal of the matrix representing inner product should be symmetric.
jesshuifeng
because <u,v> = <v,u>. So it has to be symmetric
atomicapple0
communicativity of inner prouduct!
aka
u dot v = v dot u
idkLinearAlgebra
<u,v>=<v,u>
coolbreeze
Let's take two 2D vectors for example. Any inner product <u,v> can be represented by au1v1 + bu1v2 + cu2v1 + du2v2. When we change from <u,v> to <v,u>, the result should be the same but now the representation is av1u1 + bv1u2 + cv2u1 + dv2u2. So we have au1v1 + bu1v2 + cu2v1 + du2v2 = av1u1 + bv1u2 + cv2u1 + dv2u2. And we can know that b=c. That's the elements which are not on the diagonal of the 2-D matrix. So the matrix is symmetric. And the situation is the same in higher dimension.
ccjeff
Because the inner product is commutative
winstonc
The inner product is commutative
emm
The inner product remains the same whether it is <u, v> or <v, u>, thus the matrix that represents it must be symmetric.
zhengsef
The inner product in vector space is commutative. Therefore, <u,v> = <v,u>. Then the matrix form should also be symmetric.
haotingl
because <u,v> equals <v,u>
banana
Since the order of the vectors doesn't matter this is reflected by the matrix being symmetric.
weitingt
because <u, v> should've been equal to <v, u>.
jennamil
<u,v> is equal to <v,u>
jblee
<u, v> = <v, u>
idk
The matrix representing inner product is always symmetric because <u,v> = <v,u>
alexz2
inner product is commutative
evelynk
because inner product is symmetric
sank
inner product is commutative
verylostpenguin
Since the inner product is commutative, the matrix is symmetric
I guess it's because u dot v should be equal to v dot u, so the things not on the diagonal of the matrix representing inner product should be symmetric.
because <u,v> = <v,u>. So it has to be symmetric
communicativity of inner prouduct!
u dot v = v dot u
<u,v>=<v,u>
Let's take two 2D vectors for example. Any inner product <u,v> can be represented by au1v1 + bu1v2 + cu2v1 + du2v2. When we change from <u,v> to <v,u>, the result should be the same but now the representation is av1u1 + bv1u2 + cv2u1 + dv2u2. So we have au1v1 + bu1v2 + cu2v1 + du2v2 = av1u1 + bv1u2 + cv2u1 + dv2u2. And we can know that b=c. That's the elements which are not on the diagonal of the 2-D matrix. So the matrix is symmetric. And the situation is the same in higher dimension.
Because the inner product is commutative
The inner product is commutative
The inner product remains the same whether it is <u, v> or <v, u>, thus the matrix that represents it must be symmetric.
The inner product in vector space is commutative. Therefore, <u,v> = <v,u>. Then the matrix form should also be symmetric.
because <u,v> equals <v,u>
Since the order of the vectors doesn't matter this is reflected by the matrix being symmetric.
because <u, v> should've been equal to <v, u>.
<u,v> is equal to <v,u>
<u, v> = <v, u>
The matrix representing inner product is always symmetric because <u,v> = <v,u>
inner product is commutative
because inner product is symmetric
inner product is commutative
Since the inner product is commutative, the matrix is symmetric
commutativity of inner product
Yes
YES
<u,v> = <v,u>
<u,v>=<v,u>
Because u.v = v.u