Matrices and Determinants

Matrices


Definitions, operations : addition, external multiplication, internal multiplication, properties,


Rank of a matrix, practical determination of rank,


Invertible matrix, linear group, practical calculation of the inverse of a matrix,


Change of bases, passage matrix, base change formulas for vectors and linear applications




Determinants


n-Linear forms, symmetric, antisymmetric, alternating,


Determinant of a family of n vectors relative to a basis,


Determinant of an endomorphism,


Determinant of a square matrix,


Practical calculation of a determinant, calculation techniques and development according to a row or column, notion of minor, cofactor, comatrix,


Applications of determinants : characterizing bijectivity, calculating the inverse of a matrix