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Chapter 8: Q19E (page 413)

All positive definite matrices are invertible.

Short Answer

Expert verified

The given statement is TRUE.

Step by step solution

01

Check whether the given statement is TRUE or FALSE

It is known that a matrix is positive definite if its Eigenvalues are positive.

Also, there are no entries in the diagonal zero. So, no row of the given matrix can be made zero which means all the row of the matrix are linearly independent.

Moreover, a matrix A is not invertible if 0 is an Eigen value of A.

Now,A is positive definite implies all Eigen values of A are positive, in particular they are non-zero. Hence, must be invertible.

02

Final Answer

The given statement is TRUE.

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