Matrices - An Introduction

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Quantitative Foundations for International Business

158 calificaciones

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University of London

Quantitative Foundations for International Business

158 calificaciones

Curso 3 de 6 en SpecializationInternational Business Essentials

This course provides the essential mathematics required to succeed in the finance and economics related modules of the Global MBA, including equations, functions, derivatives, and matrices. You can test your understanding with quizzes and worksheets, while more advanced content will be available if you want to push yourself. This course forms part of a specialisation from the University of London designed to help you develop and build the essential business, academic, and cultural skills necessary to succeed in international business, or in further study. If completed successfully, your certificate from this specialisation can also be used as part of the application process for the University of London Global MBA programme, particularly for early career applicants. If you would like more information about the Global MBA, please visit https://mba.london.ac.uk/. This course is endorsed by CMI

De la lección

Matrices

The analysis and even the comprehension of systems of linear equations is much easier when we use key mathematic concepts such as matrices, vectors, and determinants. This week, we’ll introduce these concepts and explain their application to economic models

Matrices - An Introduction2:51

1. What Is A Matrix?4:43

2. The Square Matrix1:38

3. Matrix Operations1:24

3.1. Addition3:33

3.2. Subtraction1:24

3.3. Scalar Multiplication1:40

3.4. Multiplication of Matrices3:41

3.5. Multiplication Procedure3:35

3.6. General Rules for Matrix Addition and Multiplication by Scalars0:53

4. The Inverse2:46

5. The Transpose2:30

6. Identity Matrix3:21

6.1. Properties of the Identity Matrix2:03

7. Linear Systems of Equation4:20

Matrices | Summary2:58

Conoce a los instructores

George Kapetanios
Professor of Finance and Econometrics
King's College London

[MUSIC]

Hello, everyone, and welcome to the fourth lecture of the Quantitative Foundations

for International Business MOOC.

This week is devoted to the idea of using matrices and

vectors to represent economic, financial and business problems.

In real world applications, most of the mathematical models used,

involve many equations.

Examples abound.

Dynamical systems describing weather patterns and

planetary movement, require complex math equation models.

Closer to home, in an example where we want to consider how inflation and

interest rates are determined.

A model would involve at least two, and sometimes up to ten equations,

describing the evolution of microeconomic variables such as unemployment, and

gross domestic product, as well as inflation and interest rates.

Usually, these equations contain many endogenous variables, and

describe the mechanisms through which these variables

depend upon several exogenous variables.

In case these equations are linear,

then a branch of mathematics called linear algebra can be used to solve them.

Even if the equations are non-linear, a lot can be learned from linear

approximations of this system of non-linear equations.

This is why these models are at the center of modern economic,

econometric and financial analysis.

Linear algebra, then is available to help us.

The consideration and analysis of sets of linear equations is much easier if we

use some key mathematical concepts such as matrices and vectors.

These are the subject matter of linear algebra.

Of course, linear algebra is applicable elsewhere as well.

For example, in the theory of differential and difference equations,

in optimizations theory, and of course, statistics and trigonometrics.

So the aim this week, is to provide the basic concepts of matrices,

which will constitute the key starting point for

further study on matrices and practical applications.

We will stress the importance of concepts such as the matrix dimension,

to understand the basic calculation rules involved in the manipulation of matrices.

Thank you very much.

[MUSIC]

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