MATRIX VERSUS VECTOR

REVISED: Sunday, March 3, 2013

You will learn the difference between a Matrix versus a Vector.

I.  MATRIX

A matrix is a rectangular array of numbers written between square brackets [  ].

The dimension of a matrix is written as the number of rows times the number of columns.

A matrix gives you a way to organize, index, and access lots of data.

A matrix is identified rows by columns.

Matrix A_ij is shown below:

  C¹ C²  C³  C⁴
  1   2    3    4  R¹
  5   6    7    8  R²
  9   1    2    3  R³

The above is a three row four column matrix or 3x4 or
R^3x4.

Matrix elements or entries inside the matrix A_ij are referred to as i^th row j^th column.

Matrix names are upper case.

II.  VECTOR

A vector is a special case of a matrix.

A vector is a matrix that only has one column.

Shown below is the three dimensional vector x_i, meaning it has three rows and one column.

C¹
1    R¹
5    R²
9    R³

The above  three row one column matrix is a special case of a matrix, called a vector.  It is 3x1 or a three dimensional vector R³.

Vector elements or entries inside vector x_i are referred to as i^th row.

There are two generally accepted ways to index a vector; they are called 1-index and 0-index.  The difference is the starting number used for the index.  If you are using modern day computer programs, most computer programs index starting with zero.  If whoever created the vector did not use modern day computer programs they will index starting with 1.

Vector names are lower case.

You have learned the difference between a Matrix versus a Vector.

Elcric Otto Circle

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