Basic operation on matrices

Basic operation on matrices such as addition, subtraction, multiplication.

MATLAB, which stands for MATrix LABoratory, is a state-of-the-art mathematical software package, which is used extensively in both academia and industry. It is an interactive program for numerical computation and data visualization, which along with its

programming capabilities provides a very useful tool for almost all areas of science and engineering. Unlike other mathematical packages, such as MAPLE or MATHEMATICA, MATLAB cannot perform symbolic manipulations without the use of additional Toolboxes. It remains however, one of the leading software packages for numerical computation. As you might guess from its name, MATLAB deals mainly with matrices. A scalar is a 1-by-1 matrix and a row vector of length say 5, is a 1-by-5 matrix.. One of the many advantages of MATLAB is the natural notation used. It looks a lot like the notation that you encounter in a linear algebra. This makes the use of the program especially easy and it is what makes MATLAB a natural choice for numerical computations. The purpose of this experiment is to familiarize MATLAB, by introducing the basic features and commands of the program.

Built in Functions:

1. Scalar Functions: Certain MATLAB functions are essentially used on scalars, but operate element-wise when applied to a matrix (or vector). They are summarized below.

1. sin - trigonometric sine

2. cos - trigonometric cosine

3. tan - trigonometric tangent

4. asin - trigonometric inverse sine (arcsine)

5. acos - trigonometric inverse cosine (arccosine)

6. atan - trigonometric inverse tangent (arctangent)

7. exp - exponential

8. log - natural logarithm

9. abs - absolute value

10. sqrt - square root

11. rem - remainder

12. round - round towards nearest integer

13. floor - round towards negative infinity

14. ceil - round towards positive infinity

2. Vector Functions: Other MATLAB functions operate essentially on vectors returning a scalar value. Some of these functions are given below.

1. max largest component : get the row in which the maximum element lies

2. min smallest component

3. length length of a vector

4. sort sort in ascending order

5. sum sum of elements

6. prod product of elements

7. median median value

8. mean mean value std standard deviation

3. Matrix Functions: Much of MATLAB‟ s power comes from its matrix functions. These can be further separated into two sub-categories. The first one consists of convenient matrix building functions, some of which are given below.

1. eye - identity matrix

2. zeros - matrix of zeros

3. ones - matrix of ones

4. diag - extract diagonal of a matrix or create diagonal matrices

5. triu - upper triangular part of a matrix

6. tril - lower triangular part of a matrix

7. rand - randomly generated matrix

Commands in the second sub-category of matrix functions are:

1. size size of a matrix

2. det determinant of a square matrix

3. inv inverse of a matrix

4. rank rank of a matrix

5. rref reduced row echelon form

6. eig eigenvalues and eigenvectors

7. poly characteristic polynomial