1. What is the coefficient matrix for the quadratic form q(x,y)=x^2+6xy+7y^2? 2. Is the quadratic form q(x,y)=x^2+6xy+7y^2 positive definite? 3. How

1. What is the coefficient matrix for the quadratic form q(x,y)=x^2+6xy+7y^2?

2. Is the quadratic form q(x,y)=x^2+6xy+7y^2 positive definite?

3. How to judge a matrix is positive definite?

4. If v and w are two vectors in a complex vector space and their inner product <v,w>=3+4i, then <w,v> is ？

5. The Hermitian dot product of two vectors [1+i, 2]T and [-3i, 4]T is equal to?