HPLC-DAD

HPLC-DAD data t w t 2 Cw 2 S = Suppose in a chromatogram obtained with a HPLC-DAD there is a peak which an impurity is co-eluted with analyte and you know analyte. Apply orthogonal projection concept and obtain the chromatographic profile of impurity.

HPLC-DAD m.file

? Apply the HPLC-DAD m.file on noised data and check the accuracy of the method

From a geometrical point of view, we can interpret a matrix with n rows and p columns either as a pattern of n points in a p-dimensional space, or as a pattern of p points in n-dimensional space Matrices p n … …

Two vectors in a three dimensional space Three vectors in a two dimensional space

p n xiTxiT xjxj x ij PpPp SnSn vnvn v1v1 vivi PnPn SpSp upup u1u1 ujuj xixi xjxj Geometrical interpretation of an n x p matrix X

p n X The rank of matrix X is equal to the number of linearly independent vectors from which all p columns of X can be constructed as their linear combination Geometrically, the rank of pattern of p point can be seen as the minimum number of dimension that is required to represent the p point in the pattern together with origin of space rank(P p ) = rank(P n ) = rank(X) < min (n, p) Rank

Rank of the real chemical matrix  Conc. s 2 = 2s 1 s1s s2s l 3 = 3l 1 l 2 = 2l 1 rank of a ideal chemical matrix = number of chemical species

Determination of rank with MATLAB

Anal.m file Constructing the data matrix for further analysis

? Apply the anal m.file and determine the rank of an absorbance data matrix which created from several three component mixtures

Rank Annihilation Methods A B k [A]=[A] 0 exp(-kt) [B]=[A] 0 (1 - exp(-kt)) A=  A [A] +  B [B] = A [A] [B] AA BB A A [A] = + [A] AA A [B] BB [B] =+

= + = + =

= - rank(A)=2rank(D)=1 rank(F)=1 A A [A] - = F - =

Kin.m file

? Simply modify the Kin.m file and show that using the spectrum of product component instead of reagent, can not decrease the rank of data

? Does the rank of matrix F decrease if the applied spectrum of the reagent is not correct in its intensities?