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Matrices

Hasse Diagrams

(a) List the ordered pairs that belong to the relation. My ANS: (a,a),(b,a)(b,b),(c,a),(c,b),(c,c),(d,a),(d,b)(d,d) (b) Find the (boolean) matrix of the relation. < my answer file attached as Mr.jpg> I did review another answer posted along the same question, but uses a different shape. I think my matrix is correct bas

Normal matrices proof

(See attached file for full problem description) --- Suppose that A, B, and AB are normal matrices. Prove that BA is also normal. Here some hints: the trace of matrices can be used in clever ways to prove equalities. Note that tr(A+B)=tr(A) + tr(B), tr(AB)=tr(BA) for any square A and B, and tr (C*C) 0 with equality if a

Groups rings and fields

Please help with the following questions: B7 Define what it means for a group to be cyclic.....

Self-Adjoint Sets

4.1. If A, B are bounded operators on H, show that (AB)*= B*A*. Even if A, B are both self-adjoint, the product AB may not be.

Multiplicative groups

(See attached file for full problem description) --- a) Recall the following definitions of the multiplicative groups GLn(k) and SLn(k) over a field k: GLn(k)={invertible n x n matrices over k} SLn(k)={A in GLn(k) such that the determinant of A=1} Prove th

Matrices : Least-squares fitting of a matrix to a curve.

Setup a 3x3 matrix equation with solution [A B C]T provides a least squares fit of the n data points: (t1, b1),...,(tn,bn) to the curve of form f(t) = A + Bsin(t) + Ccos(t) Please use the ATAx = ATb linear algebra/matrix way of doing it. ---

Multiple Choice and some to show work/matrices

This has multiple choice answers as well as some that need some written work. The attachment shows exactly what it needs. Thanks for the time. Please Answer the following questions, some are multiple choice, others require some work. 1. Write the augmented matrix for the given system: 2. Use the system in pro

Proof : Adjoints and Sturm-Liouville Theorem

1. Let's define the operator M as follows: Mu = f(x) u'' + g(x) u' + h(x) u Now define the adjoint of M as M* and let M*v = (fv)'' - (gv)' + hv = fv'' + (2f' - g)v' + (f'' - g' + h)v Show that (M*)* = M

Determinant Functions and n-Linear Functions

Each of the following expressions defines a function D on the set of matrices over the field of real numbers. In which of these cases is D a 3-linear function? Justify your conclusions. a) D(A) = A11 + A22 + A33 b) D(A) = A11 A22 A33 Recall: Let K be a commutative ring with identity, n a positive integer, and let D

Determine coding matrix using java

Coding Theory Program -------------------------------------------------------------------------------- I have attached the specifications --> Program2.doc. I need it written in Java. I have also attached --> Program 2 Defined This will help with understanding the program. The words must be generated using matrix mult

Matrix and area of a triangle

Determinates a) In the accompanying figure, the area of the triangle ABC can be expressed as area ABC = area ADEC + area CEFB - area ADFB Use this and the fact the area of a trapezoid equals 1/2 the altitude times the sum of the parallel sides to show that: (see attached filed) Note: In the derivation of this form

Derivative of a matrix

Show that if f1(x), f2(x), g1(x) and g2(x) are differentiable functions, and if W = |f1(x) f2(x)| |g1(x) g2(x)| then dW/dx = |f'1(x) f'2(x)| |g1(x) g2(x) | + |f1(x) f2(x)| |g'1(x) g'2(x)|

Similar matrices and trace proof

(See attached file for full problem description with symbols) --- If A and B are matrices over the field F, show that the Now show that similar matrices have the same trace. Recall: Let A and B are matrices over the field F. We say that B is similar to A over F if there is an invertible matrix P over F such that . -

Matrix relative to a basis for a linear transformation.

--- Let be the linear transformation defined by . a) If is the standard ordered basis for and is the standard ordered basis for what is the matrix of T relative to the pair b) If and , where , , , , what is the matrix T relative to the pair --- See attached file for full problem description.

Parity check code-Generating matrix

I need help with writing a program that will generate message words (in 0's and 1's) and then compute the code words (in 0's and 1's). Ex: Generating Matrix for the (3,4) Parity check code: 100 1 010 1 001 1 derived from using the identity matrix and then solving for x,y,z in the 4th column Message words Code w

Triangles and matrices

Researchers at the National Interagency Fire Center in Boise, Idaho coordinate many of the firefighting efforts necessary to battle wildfires in the western United States. In an effort to dispatch firefighters for containment, scientists and meteorologists attempt to forecast the direction of the fires. Some of this data can be