Applied Mathematics 1411A/B Lecture Notes - Lecture 5: Invertible Matrix, Laplace Expansion, Chemical Equation

• School: Western University
• Department: Applied Mathematics
• Course: Applied Mathematics 1411A/B
• Professor: Natalia Kiriushcheva

Document Summary

Recall: we"ve spent a lot of time talking about how to work with matrices. Definition: a square matrix in which all the entries off the main diagonal are zero is called a diagonal matrix. Note: inverses and powers of a diagonal matrix are intuitive, but for a detailed explanation, refer to the text. Examples: given the matrix below, find a3 and a-1. Definition: a square matrix in which all the entries above the main diagonal are zero is called a lower triangular matrix. A square matrix in which all the entries below the main diagonal are zero is called upper triangular. A matrix that is either upper triangular or lower triangular is called triangular. Definition: a square matrix a is called symmetric if. Theorem (symmetric matrices): if a and b are symmetric matrices with the same size, and k is any scalar, then: Caution: but the product of symmetric matrices is not always symmetric!!