Types of Matrix (Especially for GATE-Geospatial 2022)

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There are four different types of matrix:

1. Matrix Notation

Metrics are usually designated with a single capital letter, such as M. For example, one matrix of having and

One value in the matrix M would be specified by its positions, which is its row and column in the matrix. One element of the array is designated with a lower-case letter and its position

A one-dimensional matrix, having one column is one of many kinds of vectors. With column vectors, it is simpler to use only one number to designate the position. In the following matrix:

2. Matrix Transposition

The transposition of a 2D matrix yields a matrix of the same size, in which . The transposition of a matrix is derived by interchanging its rows and columns. Transposition is denoted by T.

Let us define a matrix, A. the transport of (denoted ) is such that the rows are made into columns and vice versa.

Transpose of

3. Summation of Matrix Elements

Summation of matrix elements has several forms.

For example, the notation

Is the sum of all values of , ranging from 1 to 10, which equals

Similarly, the values I may be a subscript, which denotes an ordered set of values. For example, if the variable has four values like

Then, the notation

is the sum of all values of , ranging from to , which equals:

If we want to sum all the elements of the following matrix: G

We may write,

4. Matrix Multiplication

A simple example of the application of matrix multiplication is a first-order transformation matrix. The coefficients are stored in a matrix.

C

If,

Where,

and source coordinates

and rectified coordinates

The, the coefficients of the transformation matrix are as mentioned earlier.

This could be expressed by a matrix equation, or

Where

S = a matrix of the source coordinates

C = the transformation matrix

R = the matrix of rectified coordinates

The formula for multiplying two matrices is

Where

a row in the product matrix

a column in the product matrix

an matrix

an matrix

an matrix

For every from 1 to

For every from 1 to

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