# Vector vs Matrix: Difference and Comparison

Vector and Matrix are Mathematical quantities used in linear algebra. Vector is a quantity that includes magnitude and direction like velocity, and displacement.

## Key Takeaways

1. Vectors represent one-dimensional arrays, while matrices represent two-dimensional arrays.
2. Vectors are used in physics to describe direction and magnitude, whereas matrices are used for data organization and solving linear equations.
3. Matrix multiplication is more complex than vector multiplication, involving multiple operations and elements.

## Vector vs Matrix

A vector is used to describe a one-dimensional array of numbers. Vectors have a length, which is the number of elements in the array. A matrix is used to describe a two-dimensional array of numbers arranged in rows and columns. matrices have a size, which is the number of rows and columns.

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Education Quiz

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Which of the following is NOT a 21st-century skill?

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Which branch of mathematics deals with the study of shapes and sizes of objects?

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Which is the first country to have a public education system?

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In which year was the first college in the United States founded?

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Who wrote the play "Hamlet"?

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What is the name of the first university established in the world?

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What is the capital of the country France?

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Who invented the light bulb?

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Who is known as the father of modern physics?

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What is the study of light and color called?

A vector is a quantity that is represented by a letter with an arrow on top to distinguish it from other mathematical quantities. It represents magnitude and direction.

Matrix is denoted by upper case letters in brackets or parentheses. It is a rectangular array of numbers with elements or entries in it. It has a row vector and column vector, which forms a matrix.

## What is Vector?

A vector is defined as a quantity of an object that has both magnitude and direction. It is denoted by a letter with an arrow on it.

Vector is very important in mathematics and physics in various domains like linear algebra. A vector can be combined with another vector with its head attached to the other vector’s tail.

The addition of two or more vectors results in the same magnitude and direction according to the cumulative and associative law, which is the same for the subtraction of vectors as well.

Vector can be used to find the direction of the motion of the object and how gravity is implied on an object, used in oscillators, quantum mechanics, and fluid mechanics, in the theory of relativity, the motion of an object across a plane is used in wave propagation, sound propagation helps in determining the force applied in a three-dimensional object.

## What is Matrix?

A matrix is a rectangular array of numbers or elements, or entries arranged in rows and columns. They are denoted by letters written in upper case.

A Matrix in its plural form is known as Matrices. The size of the matrix is indicated as row x columns, which is written as n x m where n denotes rows and m denotes columns in the matrix.

If the elements above or below the principal diagonal of a square matrix are zero is known as a triangular matrix, if the elements below the principal diagonal are zero, then it is known as Upper Triangular Matrix, if the elements above the principal diagonal are zero, then it is known as Lower Triangular Matrix.

The matrix in which the number of rows is greater than the number of columns is known as a Vertical Matrix, if the number of columns is greater than the number of rows, then it is called a Horizontal Matrix.

## Main Differences Between Vector and Matrix

1. Vectors have a single index in the rectangular array, whereas Matrix has two indices in their formation.
2. Vectors do not change in their magnitude and direction in their mathematical operations, whereas a Matrix changes in its magnitude in mathematical operations such as multiplicative operations with respect to associative and cumulative laws.
References

Last Updated : 19 August, 2023

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