ABSTRACT
This chapter introduces the theory of biplot through examining the process of matrix multiplication. A rank-two matrix results from multiplying one matrix with two columns with another matrix with two rows. A biplot displays a rank-two matrix through plotting its two component matrices in a scatter diagram. A biplot not only displays the two component matrices but also the product matrix, though implicitly. The elements of the product matrix are recovered through the inner-product property of the biplot. Moreover, a biplot allows visualization of the product matrix from all perspectives. These include:
Ranking of the rows in each column
Ranking of the columns in each row
Comparison of two rows for all columns
Comparison of two columns for all rows
Identification of the largest value (row) within each column
Identification of the largest value (column) within each row
Visualization of the interrelationships among rows
Visualization of the interrelationships among columns
These form the basis for visualizing two-way datasets. If the mathematics looks complicated, one may just skip this chapter. Nevertheless, it will not hinder one’s ability to understand and apply the genotype and genotype-by-interaction (GGE) biplot methodology to one’s data.
