Upload
others
View
3
Download
0
Embed Size (px)
Citation preview
Solution
Solution
Solution
Let us first find an orthogonal basis for W
Now, to avoid fractions in our computation, let us consider 3w2, instead of
w2. Note that the scaling does not change the orthogonality.
We have
Now it suffices to normalize the vectors w1, 3w2 to obtain an orthonormal
basis. Therefore, the set
Problem
Solution
Given 2x2 +12xy +20y2 is positive definite ?
Solution
The matrix
Is positive definite – its determinant is 4 and its trace is 22 so its eigenvalues are positive
Problem