Matrix Theory

Show that Null (A) and Im(A) are not orthogonal. (see Matrix in attached file)

Matrix Theory

Prove that A is normal if and only if A-A^* and A+A^* commute.

Matrix Theory

Show that each matrix type is normal. 1. Hermitian 2. skew-Hermitian 3. unitary 4. symmetric 5. skew-symmetric 6. orthogonal

Understanding the works of Gerhard Gentzen.

What are Gerhard Gentzen's mathematical accomplishments?

Solving for x using logs.

Solve for x: (2.3)^x=11

Matrix Theory

A)Verify that conjugation by matrices defines a group action of U(n) on the set of normal matrices. B)Find a representative for each orbit in (A)

Matrix Theory

(A)Show that if A is Hermitian, then iA is skew-Hermitian. (B)Show that if {Av,v} is imaginary for all v in V, then A is skew-Hermitian.

Matrix Theory

Show that the determinant of a a)real skew-symmetric matrix is non-negative, b)Hermitian matrix is real, and c)skew-Hermitian matrix is either real or imaginary.

Matrix Theory

A) Let A be a positive definite matrix. Show that X has a unique positive square root. That is, show that there exists a unique positive matrix X such that X^2 =A. B) How many square roots can a positive definite matrix have?

Matrix Theory

Please explain the following: (A) Show that if A is Hermitian, then iA is skew-Hermitian. (B) Show that if {Av,v} is imaginary for all v in V, then A is skew-Hermitian.