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Matrix Algebra with Scilab

The document provides 10 matrix algebra problems and their solutions using Scilab code. It gives the problems, code to solve each problem, and displays the output answers. The problems include finding inverses, adding/multiplying/subtracting matrices, powers of matrices, eigenvalues, and determining if matrices are unitary or Hermitian.

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Shashank K
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95 views4 pages

Matrix Algebra with Scilab

The document provides 10 matrix algebra problems and their solutions using Scilab code. It gives the problems, code to solve each problem, and displays the output answers. The problems include finding inverses, adding/multiplying/subtracting matrices, powers of matrices, eigenvalues, and determining if matrices are unitary or Hermitian.

Uploaded by

Shashank K
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Advance mathematical Physics Lab

Students Name : NARESH KUMAWAT (1907061)


RAJAT KUMAR (1907062)
ANIL KUMAR (1907060)

1 AIM

Solcing some basic matrix algebra problems using Scilab.

1
//Assignment on Matrix Algebra using Scilab

// PROBLEMS
// 1 Finding inverse of matrix [3 1;4 8]
// 2 Calculating A+B,AB,A-B for two matrices A=[5 1 3;-7 1 -5;1 -1 1] and B=[1 1 2;3 2 1;2 1 3]
// 3 Calculating X=3A-4B for A=[4 -2;1 7] and B=[-1 2;6 -5]
// 4 Calculating X=A’A -2A for A=[3 -1;0 2]
// 5 Calculating A^3 for A=[4 2;-1 0]
// 6 Calculating A+B, A-B for A=[1 2;-1 0] and B=[3 2;1 -2]
// 7 Finding complex conjugate of A=[3+7i,0;2i,4-i]
// 8 Showing matrix (1/2)[1+i,1-i;1-i,1+i] is unitary
// 9 Finding Hermitian matrix out of
[1,3-i;3+i,i],[0,3-2i;3-2i,4],[2,2-i,-3i;3+i,0,1-i;3i,1+i,0],[-1 2 3;2 0 -1;3 -1 4].
// 10 Finding eigenvalues of Hermitian matrix [3,2-i,-3i;2+i,0,1-i;3i,1+i,0]

// CODE FOR PROBLEMS


//1
A=[3 1;4 8]; disp(inv(A))

//2
A=[5 1 3;-7 1 -5;1 -1 1]; B=[1 1 2;3 2
1;2 1 3];
disp(A+B) disp(A*B)
disp(A-B)

//3
A=[4 -2;1 7]; B=[-1 2;6
-5]; disp(3.*A -4.*B)

//4
A=[3 -1;0 2]; disp((A’)*A -2.*A)

//5
A=[4 2;-1 0]; disp(A.^3)

//6
A=[1 2;-1 0]; B=[3 2;1
-2]; disp(A+B) disp(A-
B)

//7 A=[3+7.*%i,0;2.*%i,4-%i];
disp(conj(A))

2
//8 A=(1/2).*[1+%i,1-%i;1-%i,1+%i]
if(A*A’==eye(2,2)) disp("Matrix is
unitary")
end

//9
A=[1,3-%i;3+%i,%i];
B=[0,3-2.*%i;3-2.*%i,4];
C=[2,2-%i,-3.*%i;3+%i,0,1-%i;3.*%i,1+%i,0]; D=[-1 2 3;2 0 -1;3
-1 4];
if(A==A’) disp("A is Hermitian")
elseif(B==B’) disp("B is
Hermitain")
elseif(C==C’) disp("C is
Hermitian")
elseif(D==D’) disp("D is
Hermitian")
end

//10 A=[3,2-%i,-3.*%i;2+%i,0,1-%i;3.*%i,1+%i,0];
disp(spec(A))

3
// (6)
//A+B= 4. 4.
// 0. -2.
//A-B= -2. 0.
// -2. 2.

// (7)
// 3. - 7.i 0.
// -2.i 4. + i

// (8)
//Matrix is unitary

// (9)
// D is Hermitian

// (10) // -
2.
// -1. // 6.

// ANSWERS

// (1)
// inverse is
// 0.4 -0.05
// -0.2 0.15

// (2)
// A+B= 6. 2. 5.
// -4. 3. -4.
// 3. 0. 4.
// AB= 14. 10. 20.
// -14. -10. -28.
// 0. 0. 4.
// A-B= 4. 0. 1.
// -10. -1. -6. // -1. -2. -2.

// (3) // 16. -14.


// -21. 41.

// (4)
// 3. -1. // -3. 1.

// (5)
// 64. 8.
// -1. 0.

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