How do I normalise the first principal component in PCA such that its scalar product is equal to 1?

Hi all,

I am running PCA on a 80x13 data matrix, in which I require the scalar product of the first principal component to equal 1. I.e if P is the first principal component, then I need:

P'P = 1

So far, I am using the Matlab stat code but I am unable to normalise the first principal component to having a scalar product that is equal to 1.

Would any of you be able to help? I would be very appreciative of any help. My Matlab code is copied below:

With kind regards,

KB

%%PCA

clc clear all

%% Load Data

filename = 'DataFinal.xlsx'; A = xlsread(filename);

% Principal Component Analysis

[n m] = size(A); %size of A

Amean = mean(A);

Astd = std(A);

% Now I seek to standardise the data normally. This will ensure that the % data is centred and rescaled. I subtract the mean and divide by the % standard deviation.

B = (A - repmat(Amean,[n 1])) ./ repmat(Astd,[n 1]);

%Alternatively we can use the Zscore function, to demean and divide by the %standard deviation

BB = zscore(A);

%Calculating the coefficients of princ components and respective variances %, done by finding eigenfunctions of sample covariance matrix

[V D] = eig(cov(B))

% V here contains the coefficients of principal components, diagonal % elements of D store the variance of respective principal components.

%Alternatively the below is a better way of calculating our principal %components and their variance.

[COEFF SCORE LATENT] = princomp(B)

%COEFF is a 13x13 square matrix %LATENT is 13x1 matrix %SCORE is 80x13 matrix (same dimensions as original time series set)

% Cumulative variance contained in first so many principal components can % be calculated as:

cumsum(var(SCORE)) / sum(var(SCORE))

% Also note all of the principal components are completely uncorrelated