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Chapter 1: Q53E (page 1)

IfAis a positive definite matrix, then the largest entry ofAmust be on the diagonal.

Short Answer

Expert verified

The given statement is FALSE.

Step by step solution

01

Step 1: Definition of positive definite matrix

A matrix is said to be positive definite matrix, when it is symmetric matrix and all its eigenvalues are positive.

02

Step 2: To Find TRUE or FALSE

Let A=27001.

Obviously, Ais an upper triangular matrix it鈥檚 eigen values and singular values are 1 and 2 and Ais thus positive definite.

The largest entry of Ahowever is not on the diagonal.

03

Step 3: Final Answer

The given statement is FALSE.

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Most popular questions from this chapter

a. Using technology, generate a random 4脳3 matrix A. (The entries may be either single-digit integers or numbers between 0 and 1, depending on the technology you are using.) Find rref(A). Repeat this experiment a few times.

b. What does the reduced row-echelon form of most 4脳3matrices look like? Explain.

If the determinants of all the principal submatrices of a symmetric 3X3matrixare negative, thenmust be negative definite.

If A is a non-zero matrix of the form [a-bba],then the rank of A must be 2.

Show that any positive definite matrix A can be written as, where B is a positive definite matrix.

Solve the linear system of equations. You may use technology.

|3x+11y+19z=-27X+23y+39z=10-4x-3y-2z=6|
See all solutions

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