ABSTRACT
This chapter uses several elements of algebra, specifically matrix calculus and the notion of spaces endowed with a distance (or a metric). It provides definitions of matrix calculus, focusing on transposition, matrix multiplication, square matrix, orthogonal matrix, and diagonalisation. A symmetric matrix has the two following properties: two eigenvectors associated with two distinct eigenvalues are orthogonal and the eigenvalues are real numbers. In factorial analysis, we work in vector spaces. The notions of distance, norm, projection and angle are essential to this type of analysis. A vector space in which a distance is defined from a scalar product is said to be Euclidean. In factorial analyses, we always work in Euclidean spaces. In data analysis, the diagonal metrics have an essential role as they are easy to interpret; this is the same as attributing a weight to each dimension of the space. However, it is also possible to define a scalar product, and thus a metric, from a nondiagonal matrix.
