Please answer all. it is related to Numerical linear Algebra

answer Numerical linear Algebra

[Dyuman Joshi]

@Kashk Any particular reason you reopened your question afte I closed it?

MATLAB Answers is not a homework solving service, if you want help, show some effort.

[Kashk]

These are just practiced questions. You just solve 1 of these. so i get an idea, how to do it. please

[Sam Chak]

@Kashk, Then you can do it over here:

https://www.mathworks.com/matlabcentral/answers/2029564-write-a-function-called-nonsingularmat-n-returning-a-real-nonsingular-matrix-of-size-n-x-n?s_tid=srchtitle

Learning to construct a function from this example should be sufficient for you to handle the rest, I guess!

[John D'Errico]

@Kashk - that you want someone to do your homework is not relevant. It is yours. You will learn by doing. Anwers is not a service to solve homework problems. I closed your other questins, and I will now be more diligent in closing your questions if posted like this, with no effort made.

And, if this really is just a practice question, then you don't really need to solve it in the first place. I will note that your other questions wee posted with demands that someone do them for you.

Answer 1

[Sam Chak]

Hi @Kashk

In reference to your posted exercise concerning the definition of MATLAB functions, I'd like to provide a straightforward example illustrating the creation of a function that yields a singular matrix of size . The "Singular Matrix" example, though informative, does not directly address any of the six questions posed in your exercise.

To comprehensively address these inquiries, you must delve into the properties of various special matrices, including the Symmetric Matrix, Invertible Matrix, Lower Triangular Matrix, Upper Triangular Matrix, Random Matrix, as well as the Booleam Matrix.

For additional guidance and exemplification, you may also peruse a selection of examples available via the following link: https://www.mathworks.com/help/matlab/ref/function.html.

Example for creating a Singular Matrix using a Function file.

Refer to Step 1 first, and then come back to Step 2.

Step 2: Call the function from the command line >>.

% -------------------------------------------------
% Ignore these 3 lines first. You need to create the function file.
% After saving the file, type these 3 lines on MATLAB Command Window.
% -------------------------------------------------
n  = 3;
A  = SingularMat(n)

A = 3×3

1 1 1 1 1 1 1 1 1

tf = logical(rank(A) < n)   % Test if matrix is singular (1:true, 0:false)

tf = logical
   1

Step 1: Create the function file.

% -------------------------------------------------
% Type the code in the MATLAB Editor and then 
% save the file using the same name, "SingularMat.m",
% in the current folder or in a folder on the MATLAB search path.
% -------------------------------------------------
function M = SingularMat(n) % Declares a function named SingularMat that accepts input n and returns output M
    % This function creates a singular matrix of size n×n
    % For more info, see https://www.mathworks.com/help/matlab/ref/ones.html
    M = ones(n);
end

[Kashk]

it is giving error. Saying Function definition are not supported in this context. Functions can only be created as locals

[Walter Roberson]

function cannot be declared at the command line.

If you are using LiveScript then see https://www.mathworks.com/help/matlab/matlab_prog/create-live-functions.html

[Sam Chak]

Hi @Kashk,

Follow the step-by-step instructions below and you will be able to say "Hello" to the world of "Functions".

Step 1: Select the "Function" cell in the drop-down list

Step 2: A template of a Function will be shown under the Editor tab.

Step 3: Write the Function file as guided on this forum thread.

Step 4: Save the Function file to the current folder.

Step 5: Save Function file as "SingularMat.m" (by default).

Step 6: If the file is saved correctly, you will notice that "untitled" is now named "SingularMat.m".

Step 7: In the Command Window, call the function "SingularMat(n)" to produce an output assigned to "A"

Answer 2

[Walter Roberson]

The identity matrix is simultaenously real, non-singular, upper triangular, and lower triangular. So code that constructs an n x n identity matrix would satisfy the first four questions.

[Kashk]

please write a code for it

[Torsten]

You don't know how to generate the n x n identity matrix ?

In this case I recommend a 2-hours online course in MATLAB for free:

https://matlabacademy.mathworks.com/details/matlab-onramp/gettingstarted

[Walter Roberson]

lookfor identity matrix

eye                            - Identity matrix
speye                          - Sparse identity matrix
Identity Matrix                - Generate matrix with ones on main diagonal and ground values elsewhere
eye                            - Create identity matrix with fixed-point properties
codistributed.speye            - Create codistributed sparse identity matrix
distributed.speye              - Create distributed sparse identity matrix
codistributed.eye              - Create codistributed identity matrix