Matrix Analysis and Applied Linear Algebra by Carl D. Meyer | 9780898714548 | 0898714540 | Holooly

Matrix Analysis and Applied Linear Algebra

880 SOLVED PROBLEMS

Question: 5.E.3.8

Explain why the Frobenius matrix norm on C^n×n must satisfy the parallelogram identity. ...

Verified Answer:

(a) As shown in Example 5.3.2, the Frobenius matri...

Question: 5.E.4.18

It was demonstrated in Example 5.4.3 that y is linearly correlated with x in the sense that y ≈ β0e + β1x if and only if the standardization vectors zx and zy are “close” in the sense that they are almost on the same line in ℜ^n. Explain why simply measuring ||zx − zy||2 does not always gauge the ...

Verified Answer:

If y is negatively correlated to x, then

z_...

Question: 5.3.2

Describe the norms that are generated by the inner products presented in Example 5.3.1. ...

Verified Answer:

• Given a nonsingular matrix

A ∈ \mathcal{C...

Question: 7.2.7

Determine the spectral projectors for A = (1 −4 −4 8 −11 −8 −8 8 5). ...

Verified Answer:

This is the diagonalizable matrix from Example 7.2...

Question: 5.4.3

Linear Correlation. Suppose that an experiment is conducted, and the resulting observations are recorded in two data vectors x = (x1 x2 … xn), y = (y1 y2 … yn), and let e = (1 1 … 1). Problem: Determine to what extent the yi’s are linearly related to the xi’s. That is, measure how close y is ...

Verified Answer:

The cosine as defined in (5.4.1) does the job. [la...

Question: 7.3.3

For a scalar t, determine the matrix exponential e^At, where A = (−α β α −β) with α + β ≠ 0. ...

Verified Answer:

Solution 1: The characteristic equation for A is[l...

Question: 7.E.3.16

Let H = (1 0 0 −1 −2 −1 0 2 1). (a) Apply the “vanilla” QR iteration to H. (b) Apply the the single shift QR iteration on H. ...

Verified Answer:

(a) The “vanilla” QR iteration fails to converge. ...

Question: 7.E.3.15

Explain why the function m(v) used in the development of the power method in Example 7.3.7 is not a continuous function, so statements like m(xn) → m(x) when xn → x are not valid. Nevertheless, if lim n→∞ xn ≠ 0, then lim n→∞ m(xn) ≠ 0. ...

Verified Answer:

Consider

x_n = \begin{pmatrix}1 − 1/n\\ -...

Question: 7.E.3.13

Find a dominant eigenpair for A = (7 2 3 0 2 0 −6 −2 −2) by the power method. ...

Verified Answer:

The dominant eigenvalue is

λ_1 = 4,

...

Question: 7.E.3.11

A particular electronic device consists of a collection of switching circuits that can be either in an ON state or an OFF state. These electronic switches are allowed to change state at regular time intervals called clock cycles. Suppose that at the end of each clock cycle, 30% of the switches ...

Verified Answer:

(a) Draw a transition diagram similar to that in F...

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