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Chapter 8: Q14E (page 413)

The determinant of a negative definite4脳4matrix must be positive.

Short Answer

Expert verified

The given statement is TRUE.

Step by step solution

01

Check whether the given statement is TRUE or FALSE

The Eigen values of a negative definite matrix are negative.

Hence any 4脳4negative definite matrices will have 4 negatives (may not be distinct) Eigenvalues.

It is know that the determinant is the product of the Eigenvalues of the matrix and the product of 4 negative numbers is positive, so, the determinant of a negative definite 4脳4matrix is positive.

02

Final Answer

The given statement is TRUE.

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Most popular questions from this chapter

Consider an orthogonal matrix Rwhose first column isv鈬赌. Form the symmetric matrix A=v鈬赌v鈬赌T. Find an orthogonal matrix Sand a diagonal matrix Dsuch that S-1AS=D . Describe Sin terms ofR.

If A is an n脳nmatrix, what is the product of its singular values 蟽1,...,蟽n? State the product in terms of the determinant of A. For a 2脳2matrix A, explain this result in terms of the image of the unit circle.

Find a symmetric 2x2matrix Bsuch thatB3=15[12141433]

Show that any matrix of rank rcan be written as the sum of r matrices of rank 1.

LetLfrom R3to R3be the reflection about the line spanned by

v鈫�=[102]

a. Find an orthonormal eigenbasis for L .

b. Find the matrix B of L with respect to eigenbasis.

c. Find the matrix A of L with respect to the standard basis ofR3 .
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