Vector vs Matrix
Mathematics is used by man in the different fields that interest him. It is used in engineering, natural and social science, medicine, and other disciplines. It has been used ever since man discovered numbers and learned how to count.
It was first used by man to record time, for land measurement, in making patterns for painting and weaving, and in trading. The Egyptians and Babylonians were the first to use mathematics in taxation, construction, and astronomy, and the Greeks were the first to study mathematics as a science.
Mathematics has many fields which include geometry and algebra. Linear algebra in particular is a branch of mathematics that deals with the study of vector spaces and linear operations which are represented by a matrix or matrices.
A vector is defined as a mathematical quantity that has magnitude and direction, such as velocity. It is represented by a letter which is also what is used to represent a real number or a scalar quantity. To distinguish it from a real number, it is typed in boldface with an arrow above it. A unit vector is a vector with a magnitude of 1 and is denoted with a carat (^) above the variable.
Vectors are used in geometry to simplify three-dimensional problems, and many quantities in physics are vector quantities. A vector has the ability to simultaneously represent magnitude and direction. An example is the wind which has both speed and direction and so are other moving objects.
A matrix, on the other hand, is a rectangular array of numbers which is a key tool in linear algebra. It is used to represent linear transformations and keep track of coefficients in linear equations. Matrices are also used in physics, graph theory, computer graphics, calculus, and serialism.
An item in a matrix is called an element or an entry, and it is represented by a lower-case letter with two subscript indices. The matrix is represented by an upper-case letter and notated by brackets or parentheses.
It can have a row (row vector) or a column (column vector) which defines the components of vectors. Higher dimensional arrays of numbers or matrices define components of a generalization of a vector which is called a tensor.
Summary:
1.A matrix is a rectangular array of numbers while a vector is a mathematical quantity that has magnitude and direction.
2.A vector and a matrix are both represented by a letter with a vector typed in boldface with an arrow above it to distinguish it from real numbers while a matrix is typed in an upper-case letter.
3.Vectors are used in geometry to simplify certain 3D problems while matrices are key tools used in linear algebra.
4.A vector is an array of numbers with a single index while a matrix is an array of numbers with two indices.
5.While a vector is used to represent magnitude and direction, a matrix is used to represent linear transformations and keep track of coefficients in linear equations.