Matrix types, column symmetric

Table M4 Some matrices used as representation of the molecular structure symbol, current name, number of rows and columns (A, number of vertices 6, number of edges , cyclicity D, topological diameter and K, maximum walk length), and type (S, symmetric matrix U, unsymmetrical matrix B, symmetric or unsymmetrical matrix and D, diagonal matrix).

A square matrix is one in which the number of columns is equal to the number of rows. An important type of square matrix which arises quite often in the finite element method is a symmetric matrix. Such matrices possess the property that aij = aji- An example of such a matrix is given below ... 

Matrices of special structure like symmetric or band type matrices can be stored even more effectively. In some cases, the matrix A must not be stored at all and the elements of a single row or column can be generated during the computation (see the example at the end of this article). 

The separation and quantitation of volatile hydrocarbons is one of the most important analyses in the petrochemical applications field. Depending on the type of hydrocarbons to be analyzed and the sample matrix a certain type of column is preferred. Generally hydrocarbons are easily quantified by gas chromatography. Since the hydrocarbon molecule does not contain a large dipole these compounds elute as symmetrical peaks from most GC columns. The chemi-... 

The active compounds capsaicin and dihydrocapsaicin elute with a short retention time difference. A good separation free from peak tailing is necessary for the reliable peak integration for low RSD values at low concentration levels. It was found with different types of GC columns that the quality of the column deactivation, age of the column and matrix deposits have a detrimental effect on the capsaicin and dihydrocapsaicin peak shape and quantitative reproducibility. Also, piperine and cinnamaldehyde were affected while thymol always showed symmetrical peak shapes, apparently being unaffected by the increasingly active column film conditions. 

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