# Posts tagged ‘transpose’

I’m going to cover broad topics in vectors, matrices and the likes, so i’t may appear that i’m skipping specific’s at time. But hopefully I’ll give a good enough understanding and hopefully be able to add specifics in due course. So onto matrices:

A matrix is an object made up of columns and rows – by association an n x m is row by column matrix of n rows and m columns like so (the ** …n** just denotes the list of values):

M C O L U M N S

N ..n

R ..n

O ..n

W ..n

S ..n

Another way to look at it is that each column represents a dimension, if we have say a 3 x 3 matrix we can represent an objects orientation, with each row representing an axis:

X0 Y0 Z0

X1 Y1 Z1

X2 Y2 Z2

In this example each row is a vector (direction) with an x, y and z component and by this three dimensional. This vector is also known as a ‘row vector’, similarly if we got the first components of each row we can call that a ‘column vector. Matrices have no know bounds – theres no limit to them which makes them important in n-dimensional workflows (stuff that i dig).

There are 4 main big functions of matrices – Transpose, multiplication, determinant and inverse. These 4 are the grease that allows powerful manipulation of matrices. We’ll throw mean (average) in there two because its important in data analysis.

**Transpose**

We’ll start with something relatively simple but that’ll make a difference when we get to multiplication. All that transpose does is swap rows for columns and vice versa. So a matrix that looked like this:

1 2 3

4 5 6

Becomes this:

1 4

2 5

3 6

Doing this in pseudo code we can do something like this:

for i in column:

for j in rows:

collect rows[i][j]

So we’ve transposed the matrix, why is this important – we’ll to multiply a matrix with another matrix it needs to have the same amount of columns as the other has rows! We’ll discuss square and identity matrices next…