Let V be an n-dimensional vector space over F, and let G be a nondegenerate bili

ID: 3283742 • Letter: L

Question

Let V be an n-dimensional vector space over F, and let G be a nondegenerate bilinear form on V. a] Given any linear operator T E L(V),show that there exists a unique linear operator T E L(V) such that G(Tv, w) G(v,Tw) for all, w E V The operator Tt is called the adjoint of T with respect to the nondegenerate bilinear form G bl Show that the operation on L(V) that takes T to T satisfies the following properties: (TS)' = StTt. The above two identities say that Tt is a linear algebra anti-homomorphis of L(V) [c] If G is either sylnmetric or skew-symmetric, show that (Tt)t-T. [d] Let B = {ei, ,en} be a basis of V. Express the matrix [Tt]s in terms of [T]B and [GIB.

Explanation / Answer

Using V= V* this result follows.

We know the definition of nondegerate bilinear form

Using this

Navigate

Let V be an inner product space. For a fixed nonzero vector v_0 in V, let T. V r

Let V be the (real) vector space of all polynomial functions from R into R of de

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.

Let V be an n-dimensional vector space over F, and let G be a nondegenerate bili

Question

Explanation / Answer

Related Questions

Navigate