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1.) Proof that the following statements are equivalent 1. is an eigenvalue of for some with .
2. There exists a vector with and .
3. , where is the smallest singular value of .
4. .2.) Let be a simple eigenvalue of a diagonalizable matrix with right and left eigenvectors and , and let be the corresponding eigenvalue of the matrix . Show that to first order it holds that Hint: Consider the perturbed eigenvalue equation .
3.) Proof that for and with . Give an example for which .
Programming Exercise
1.) In the submodule scipy.linalg.blas you find a lowlevel interface to the BLAS. Use this interface to make accurate timing measurements of BLAS3 matrix matrix products for real double precision matrices of growing dimension. Plot the time against the growing dimension using a logarithmic scale in the time. (the plot command semilogy is helpful here). Also, plot the function against the dimension and compare the two. What do you observe? [5 marks] z A + δA δA ?δA?2 ≤ ? u ∈ C m ?(A - zI)u?2 ≤ ? ?u?2 = 1 σn(zI - A) ≤ ? σn A ?(zI - A) -1?2 ≥ ? -1 λ A x y λ + δλ A + δA δλ = . y δAx H y x H (A + δA)(x + δx) = (λ + δλ)(x + δx
Provide a site map of your e-commerce website in the form of a tree diagram that shows hierarchical structure of your e-commerce website
Define memory. Describe types of memory, including implicit and explicit memory and declarative and procedural memory.
How do you create a 3D array of doubles in C++
Examined the multiple access problem and its solutions., as part of our study of wireless and mobility, we are considering another solution to the same problem, namely Code Division Multiple Access (CDMA). What is CDMA, and how does it compare to oth..
draw the hieararchy chart and then plan the logice for a program that calculates a person's body mass index BMI. BMI is a statistical measure that compares the person's weight and height.
5 Pages or more, IEEE format for the paper, Try to have a suitable Title for the IEEE paper according to requirements. Make sure you include the OS listed plus the "others" Also, that all the 40 citations should be in the paper referenced. (5 onli..
From your current understanding of design, analysis, and optimization, elaborate on the relationship of analysisand optimization in the context of computational expense.
Using a PLD, develop an I/O port decoder that generates the following high-bank I/O strobes: 300DH, 300BH, 00B6H, and 00EEH.
Write the create index statements to create a clustered index on the groupid column and a nonclustered index on the individualid column of the groupmembership table.
Identify the advantages and disadvantages of using Word to work with graphics, tables, and special formatting functionality. Provide specific examples.
Consider a coin system for which we know the greedy algorithm would fail to always provide optimal change: d = [1,5,8] . Show how to use dynamic programming to optimally make change for 10 units.
Let the TCP procedure for evaluating RTT. Assume that α = 0:5. Let SampleRTT1 be the Most recent sample RTT, let SampleRTT2 be the next most recent sample.
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