Principle component analysis coefficients and standardization

I'm trying to understand the meaning of the PCA coefficient matrix. It says "Each column of coeff contains coefficients for one principal component, and the columns are in descending order of component variance."

1) Does this imply that PC1 can be constructed from the original unit space's vectors? If the first column is as follows, does that mean that PC1 and PC2 consists primarily of the first and second variable?

0,9997

0,0249

0,0026

-0,0001

0,0000

0,0000

-0,0003

2) PCA normally includes standardization. Matlab's PCA function seems to center the data, but not standardize it, is that correct? To get meaningful results should one manually center and divide by variance before performind PCA?

(data-mean(data))./var(data)

Answer 1

[Cris LaPierre]

I find this video a good explanation of PCA.

In short, principal components describe the directions of max variance of the data. The number of principal components is equal to the dimensionality of your data (e.g. 2 for 2D data).

Answer 2

[Kamal]

Hey,

I'm really struggling to understand what these terms mean inside matlab [coeff,score,latent,tsquared,explained,mu] , I consider myself to understand PCA in general and in theory (perhaps im still far far away from that), slightly far from grasping it mathemtically, but i have really spent hours and days in an attempt to understand it so i can use it in my upcoming grad project

I'm stuck now at this point where what i understood about PCA couldn't be connected to what's on matlab and how the implementation actually works

I do only understand the explained matrix where it's the total variation of each PC we got, the ones presented in the scree plot

Would really appreciate any help with other matrices