Prove that every symmetric matrix S = K + N can be written as the sum of

Question:

Prove that every symmetric matrix S = K + N can be written as the sum of a positive definite matrix K and a negative definite matrix N. Hint: Use Exercise 3.5.12(b)

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

See More Books

Question Posted: Jun 17, 2016 08:41 AM

See More Questions

Prove that every symmetric upper (or lower) triangular matrix is diagonal.
Prove that every positive definite matrix K can be written as a Gram matrix.
If an m n matrix A has rank r, prove that A can be written as the sum of r matrices, each of which has rank 1.
n Write a program that finds how many zeros in the list and puts the result in cntr variable (Copy and paste a program that is not related to the requirements will get Ox0000) .data list1 .word...
Custom Computers, Inc. from Problem 9 is considering a new ordering policy. The new order quantity would be 650 heat sinks. Recalculate Problem 9, parts (a) through (e), and compare results. (a)...
A motorist claims that the South Boro Police issue an average of 60 speeding tickets per day. These data show the number of speeding tickets issued each day for a period of one month. Assume is...
The time-dependent axial stress, $\sigma_{x}(t)$ and the time-dependent circumferential stress, $\sigma_{y}(t)$ in the wall of the filament-wound, thin-walled composite pressure vessel shown in...
At the time of her death on September 4, 2015, Alicia held the following assets. Alicia was also the life tenant of a trust (fair market value of $2 million) created by her late husband Bert. (The...
Punishments typically identified as intermediate sanctions include intensive supervision probation (ISP), drug courts, fines, community service, day reporting centers, remote-location monitoring,...
Draw the influence line for the vertical reaction and shear & moment in point c ? 4m 3m C 1m
Let |||| be any norm on Rn. (a) Show that q(x) is a positive definite quadratic form if and only if q(u) > 0 for all unit vectors, ||u|| = 1. (b) Prove that if S = ST is any symmetric matrix, then K...
(a) Prove that any regular symmetric matrix can be decomposed as a linear combination K = d1,11IT1 + d2I21T2 + ¢ ¢ ¢ + dn11lT1 (3.69) of symmetric rank 1 matrices, as Exercise 1.8.15....
Testing 100 right-handed participants on the reaction time of their left and right hands to determine if there is evidence for the claim that the right hand reacts faster than the left. Indicate...
Suppose that $A \Rightarrow B$ is true. Which is then automatically true, the converse or the contrapositive?
Let $\mathbf{F}(x, y, z)=\left\langle z^{2}, x+z, y^{2}ightangle$, and let $\mathcal{S}$ be the upper half of the ellipsoid \[ \frac{x^{2}}{4}+y^{2}+z^{2}=1 \] oriented by outward-pointing...
When are entry and exit pseudostates used?
Propositional wffs and truth tables belong to a system of two-valued logic because everything has one of two values, $\mathrm{F}$ or $\mathrm{T}$, which we can think of as 0 or 1 . In fuzzy...
Consider Table 11.1. Table 11. 1 a. If this national debt in each of the given years is shared 2009:\$36,000/ equally by the U.S. citizens, how much would it cost person; each of us (rounded to the...
The accounting clerk for Rivers Edge Canoe & Kayak prepared the income statement for the year ended December 31. The accounting supervisor at Rivers Edge noticed that the balance of the...
Why are stocks usually more risky than bonds?
Solve the following general system by inverting the coefficient matrix and using Theorem 1.6.2. x1 + 2x2 + 3x3 = b1 x1 - x2 + x3 = b2 x1 + x2 = b3 (a) b1= - 1, b2 = 3, b3 = 4 (b) b1 = - 1, b2 = -1,...
Verify Theorem 1.7.1 d for the matrices A and B in Exercise 12. Theorem 1.7.1 d The inverse of an invertible lower triangular matrix is lower triangular, and the inverse of an invertible upper...
Let A be an n n symmetric matrix. (a) Show that A2 is symmetric. (b) Show that 2A2 - 3A + I is symmetric.
Assume that in 2023, Bobby had a vacant lot that was given to him as a gift from his father that had an FMV of $40,000 and an adjusted basis of $15,000.
Show the adjusting entries that you would make given the additional data below. In addition to the formal journal entry, please also indicate the type of adjusting entry that is being made, ...
I need one to three paragraphs written about the awk command in unix. Everything should be in a power point presentation. Make sure it contains the following: Command name Description How to use the...

Prove that every symmetric matrix S = K + N can be written as the sum of

Question:

Step by Step Answer:

Write S S c I c I K N where N ...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions