PHYS 1010 Lecture 4: DETRMNTS.DOC

• School: York University
• Department: Physics and Astronomy
• Course: PHYS 1010
• Professor: Christopher Bergevin

Document Summary

There are several ways to define determinants and all have some advantages and some drawbacks. We adopt a definition that saves teaching time and makes it easier to prove some results. Recall three types of n by n elementary matrices: Obtained by interchanging two rows of i e e. Obtained by multiplying any row of i by a non zero scalar. Adding a scalar multiple of one row to another row of. Definition: for a square matrix a, determinant of a is the real number det(a) defined with det(a) = 0 if a is a singular (i. e. not inevitable) matrix following three conditions (i) (ii) det(e) = The number det(a) as defined above is unique. ( proof is based of the (iii) det(ea)= det(e)det(a) Note: fact that every nonsingular matrix has unique representation diagonal entries of triangular matrices l , u are all 1 for a proof refer to: Using this definition, usual properties of determinant can be proved easily.