Purchase Solution

Positive definite matrix

Not what you're looking for?

Ask Custom Question

Which 3 by 3 symmetric matrices A produce following functions f = X^T A X ?
Why is the first matrix positive definite but not the second one?

a) f = 2 (X1^2 + X2^2 + X3^2 - X1X2 - X2X3)

b) f = 2 (X1^2 + X2^2 + X3^2 - X1X2 - X1X3 - X2X3)

Purchase this Solution
Solution Summary

Positive definite matrix is assessed.

Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Probability Quiz

Some questions on probability

View More Free Quizzes
Related BrainMass Solutions

  • Square roots of matrix

    B) How many square roots can a positive definite matrix have? See attachment Problem: A) Let A be a positive definite matrix. Show that X has a unique positive square root.

  • Linear Algebra : An SPD Matrix and Inverse

    66715 Linear Algebra : SPD Matrix and Inverse Let A be a symmetric and positive definite (SPD) matrix. Is A^-1 ( inverse of matrix A) a SPD matrix? If so, prove it. If not, explain and give an example.

  • Matrix Algebra - Definite vs. Indefinite

    We know from the matrix algebra that the associated quadratic form {see attachment}, where x = (x1,...xn), is either positive-definite, negative- definite or indefinite. Now assume the diagonal entries of A are all zero.

  • Linear Algebra : Orthogonal Basis

    An n x n matrix A with entries from R or C is called positive definite if is positive definite. Please represent the quadratic form by a symmetric matrix. And verify that Q positive definite. Thank you.

  • LU factorisation

    0) that does not satisfy the requirement x^T Ax > 0. ** Please see the attached file for the complete solution ** This solution explains the steps to LU factorization and how to show that the matrix is not positive definite.

  • Finding critical points, extreme values and saddle points. f(x,y)=x3+3xy2-3x2-3y2+4.

    Since is positive definite matrix, then is an extreme minimum point with value and are not definite. So and are saddle points. Critical points, extrema and saddle points are found. The solution is detailed and well presented.

  • Vectors, matrices, and baces

    This is the definition of a positive definite matrix, so that matrix A must be positive definite in order for xTAy to be an inner product. Answer 3 a) If B={u1, u2,...

  • 2x2 Symmetric Matrix with Positive Eigenvalues.

    517973 Symmetric Matrix with Positive Eigenvalues Suppose that both eigenvalues of a 2 x 2 symmetric matrix B are positive. Which of the following statements are true? i) The system Bx = b has a unique solution for each b.

  • Normal Distribution - Linear Model Problem

    where Using the spectral theorem It follows from the spectral theorem of linear algebra that a positive-definite symmetric matrix S has a unique positive-definite symmetric square root S1/2.

View More Related Solutions