29 Questions
What is the result of multiplying the transpose of an orthogonal matrix by itself?
An identity matrix
What is the type of matrix R in the QR decomposition A = QR?
Upper triangular matrix
What is the condition for the uniqueness of the QR decomposition of a matrix A?
A is a nonsingular matrix
What is the purpose of the Gram-Schmidt process in the QR decomposition?
To orthogonalize a set of vectors
What is the matrix Q in the QR decomposition of a matrix A?
An orthogonal matrix
What is the MATLAB command to initiate a matrix of zeros with 3 rows and 3 columns?
Q=zeros(3,3)
What happens when an expression returns a result that is not assigned to any variable?
The system assigns it to a variable named answer
What is the purpose of the 'who' command in MATLAB?
To display the names of all variables
What is the default display format for numbers in MATLAB?
Four decimal place values
What happens when you use the 'clear' command without specifying any variable in MATLAB?
It deletes all variables from the memory
How can you extend a long assignment to another line in MATLAB?
Using a new line with the continuation of the assignment
What is the purpose of the 'whos' command in MATLAB?
To display the names and sizes of all variables
What is the purpose of the loop variable 'i' in the Matlab code for Gauss Elimination?
To iterate through the columns of the matrix
What is the output of the Gauss Elimination method for the given system of equations?
x = -1 1 2
What is the purpose of the command 'A(j,:) = A(j,:) - m*A(i,:)' in the Gauss Elimination Matlab code?
To perform the row operations
What is the name of the process used in the Matlab code to orthogonalize the matrix?
Gram-Schmidt orthogonalization
What is the purpose of the command 'x(n) = A(n,n+1)/A(n,n)' in the Gauss Elimination Matlab code?
To solve for the variable x(n)
What is the purpose of the command 'summ = summ + A(i,j)*x(j,:)' in the Gauss Elimination Matlab code?
To solve for the variable x(i)
What is the purpose of the matrix P in the context of projection matrices and least squares?
To project a vector onto another vector
What is the result of the code P*u in the provided example?
A 2x100 matrix where each column is a vector projected onto the vector v
What is the interpretation of the relative residual in the output of the lsqr function?
The ratio of the norm of the residual vector to the norm of the right-hand side vector
What is the relationship between the vectors u and v in the provided example?
u is projected onto v
What is the purpose of the hold on command in the provided code?
To hold the current plot and add new data to it
What is the primary goal of finding the least square fit for a system of equations?
To minimize the sum of the squares of the errors
What is the name of the process used to find the point on a plane that is closest to a given point?
Projection
What is the purpose of computing the SVD of a matrix?
To diagonalize the matrix
What is the correct order of steps to compute the SVD of a matrix A?
Find AAT, find eigenvalues, find eigenvectors, normalize them
What is the relationship between the singular values and eigenvalues of a matrix A?
σ1 = λ1 and σ2 = λ2
What is the purpose of normalizing the eigenvectors in the SVD process?
To make the eigenvectors orthonormal
Understand how to work with variables in MATLAB, including assigning values, using previous results, and multiple assignments on the same line. Learn how to use the 'answer' variable and more!
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