If A is a positive semi-definite matrix, then A^2 + 2I is: (a) Positive semi-definite (b) Positive definite (c) Negative definite (d) None of the above
Added by Leslie L.
Step 1
A matrix A is positive semi-definite if for any non-zero vector x, the quadratic form x'Ax is greater than or equal to zero, where x' denotes the transpose of x. Show more…
Show all steps
Close
Your feedback will help us improve your experience
Mengchun Cai and 98 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Determine whether each of the following matrices is positive definite, positive semi-definite, negative semi-definite, negative definite, or indefinite. (Recall that a matrix is positive definite if x T Ax > 0 for all x , positive semidefinite if x T Ax ≥ 0 for all x , negative semidefinite if x T Ax ≤ 0 for all x , negative definite if x T Ax < 0 for all x , and is otherwise indefinite.) A1 = [1 0 0; 0 2 1; 0 1 2], A2 = [1 0 0; 0 2 -1; 0 -1 2], A3 = [1 0 0; 0 -2 1; 0 1 -2]
Madhur L.
determine by inspection whether the matrix is positive definite, negative definite, indefinite, positive semidefinite, or negative semidefinite. (a) $\left[\begin{array}{ll}1 & 0 \\ 0 & 2\end{array}\right]$ (b) $\left[\begin{array}{rr}-1 & 0 \\ 0 & -2\end{array}\right]$ (c) $\left[\begin{array}{rr}-1 & 0 \\ 0 & 2\end{array}\right]$ (d) $\left[\begin{array}{ll}1 & 0 \\ 0 & 0\end{array}\right]$ (e) $\left[\begin{array}{rr}0 & 0 \\ 0 & -2\end{array}\right]$
Diagonalization and Quadratic Forms
Quadratic Forms
Decide whether the matrix below is positive definite, positive semidefinite, negative definite, or neither
Sri K.
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD