Matrix construction and operations

OBJECTIVE:

To study basic matrix constructors and operations using Scilab.

SOURCE CODE:

Matrix Constructors:

zeros(3,2)

//

// ans =

//    0.    0.

//    0.    0.

//    0.    0.

eye(2,3)

//

// ans =

//    1.    0.    0.

//    0.    1.    0.

ones(2,2)

//

// ans =

//    1.    1.

//    1.    1.

rand(4,4)

//

// Random 4x4 matrix with values in [0,1]

Matrix Y:

Y = [1 4 6;

     2 7 3;

     4 1 1];

Basic Operations:

max(Y)       // Maximum element

min(Y)       // Minimum element

sum(Y)       // Sum of all elements (use sum(Y(:)) if needed)

prod(Y)      // Product of all elements

Mathematical Functions:

sin(Y)

cos(Y)

tan(Y)

asin(Y)

acos(Y)

exp(Y)

log(Y)       // Natural log

log10(Y)     // Log base 10

sqrt(Y)      // Square root

Floating-Point Functions:

ceil(Y)

floor(Y)

round(Y)

fix(Y)       // Truncates values toward zero

nthroot(Y, 4)   // 4th root of elements (custom function may be needed in older versions)

Sign Function:

sign(Y)

//

// ans =

//    1.    1.    1.

//    1.    1.    1.

//    1.    1.    1.

Modulo Operations:

modulo(10, 3)        // Returns remainder

pmodulo(10, 3)       // Returns positive remainder (Scilab specific)

Concatenation:

Z = [9 8 7;

     5 6 4;

     3 2 1];

cat(1, Y, Z)     // Row-wise concatenation

cat(2, Y, Z)     // Column-wise concatenation

Matrix Analysis:

A = [1 -2;

     -2 0];

det(A)           // Determinant

rank(A)          // Matrix rank

trace(A)         // Sum of diagonal elements

spec(A)          // Eigenvalues

RESULT:

Thus, the Matrix constructors and operations in Scilab are successfully executed and verified.