1. ## quadratic forms of symmetric matrices...

hi i just wanted a quick explanation of what a symmetric matrix is and what they mean by the quadratic form by the standard basis?

(1)
for example why is this a symmetric matrix

[1 3]
[3 2]

and what is the quadratic form of the matrix by the standard basis?

(2)
also how would i go about figuring out the quadratic form corresponding to the matrix by the standard basis for
[ 0 1 1]
[ 1 3 5]
[ 1 5 0]

2. Haven't you a definition of "symmetric"? $A\;=\;A^{t}$