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.

Factoring polynomial expressions.

Factor the following: a) 3y^2-3 b) 25-16x^2y^2 c) (x+y)^2-z^2 d) (x-3)^2-9 e) t^2-2t-3

Linear Algebra -- Linear Transformations

Let L be the linear transformation mapping R2 into itself defined by L(x) = (x1*cos alpha - x2*sin alpha, x1*sin alpha + x2 cos alpha)T Express x1, x2, and L(x) in terms of polar coordinates. Describe geometrically the effect of the linear transformation. Thanks very much.

Linear Algebra -- Kernel and Range

Determine the kernel and range of the following linear transformation from R^3 into R^3. L(x) = (x1, x2, 0)^T Determine the kernel and range of the following linear transformation from P3 into P3. L(p(x)) = p(x) - p'(x) Thank you!