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Matrices in Finance: Size, Shape, and Operations, Lecture notes of Finance

An introduction to matrices, their uses in mathematics, computing, and finance, and various operations such as scalar multiplication, addition, transpose, and matrix multiplication. It also covers the inverse of a matrix and its application in solving simultaneous equations.

Typology: Lecture notes

2010/2011

Uploaded on 09/14/2011

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MSc Finance,
MSc International Banking & Finance,
MSc Investment & Finance,
MSc International Accounting & Finance
Computing for Finance
and Financial Analysis
(Excel)
Lecture 6 - Week 6
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MSc Finance, MSc International Banking & Finance, MSc Investment & Finance, MSc International Accounting & Finance

Computing for Finance

and Financial Analysis

(Excel)

Lecture 6 - Week 6

Matrices A matrix is a table or array of numbers or variables Many uses in mathematics, computing and finance Examples include solving linear simultaneous equations and calculating efficient frontiers

Example (a) 3 rows x 2 columns

Example (b) 3 rows x 3 columns 3x3 square matrix

Example (d) 3 rows x 1 column 3x1 matrix a column vector

Example (e) 4 rows x 4 columns 4x4 square matrix 4x4 Identity matrix (I)

Scalar Multiplication A number * a matrix Result is the same shape as the original matrix Multiply each element in the matrix by the scalar

Scalar Multiplication In Excel: Multiply each cell in the matrix e.g. =B22 etc. Use an array formula: {=B2:C42}

Transpose Changes rows into columns and columns into rows Denoted by T or Use the =TRANSPOSE array formula This is not the same as Transpose from Paste Special

Matrix Multiplication Size and shape matters Example: A = 3x2, C = 2x 3x2 2x If these are equal, multiplication is possible Result is shape of outer two numbers

Inverse of a Matrix Inverse of a matrix A is defined as: AA*

- = I = A - *A Always a square matrix =MINVERSE(range) Can be used to solve simultaneous equations

Simultaneous Equations Translate the equations into matrices The result vector X is then the inverse of A multiplied by the vector Y X = A

- *Y =MMULT(MINVERSE(A-range),Y-range)