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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 .
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
A firm contemplating entering the market would need to invest $100 million to build a minimum efficient scale production plant (or about $10 million annually on an amortized
Show that a full subtractor can be implemented using a "Full Adder" device and two inverter gates - For this, you will have to create a "Full Adder" device (Note: you can use
1. What actions has your organization taken to unleash buying and selling power? 2. What major changes has your organization recently made to improve your buying and selling p
Write a program that reads in a list of names, allocates a new Peron for every one of them, and places them in a vector . Next, request the name of each best friend for ever
a) Write a Pseudocode to represent the logic of a program that allows the user to enter values for the width and length of a room's floor in feet. The Program outputs the area
Describe how the digital forensics function complements the overall security efforts of the organization. Evaluate the operational duties of digital forensic personnel and how
write algorithm to save few new phone numbers in the address book of cell phone. algorithm should work even if there's only one new phone number or several new phone numbers
This course introduces basic programming concepts, logic, and scripting language tools used to automate basic system administrator processes. Critical thinking, logic, and t
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