Algebra Series - Concepts and Formulas™
Matrix Fundamentals, Basic Operations on Matrices (ALG-CF16)

This sheet provides a comprehensive review of all of the most important topics, concepts and formulas fully covering matrix fundamentals and basic operations on matrices, explained in detail, with detailed illustrations. Unlike charts and notes, this Concepts and Formulas™ sheet anticipates and answers questions about how to use the concepts - how to solve problems with them, it doesn't just list facts and formulas. There is even an example, or two, for each concept, to help you to nail down the central ideas.


Topics Covered:

• The definition of Matrix (Matrices)
• Entries of a matrix
• Size of a matrix
• Order of a matrix
• Dimension of a matrix
• Row Matrices and Row Vectors
• Column Matrices and Column Vectors
• Square matrices
• The main diagonal
• The transpose of a matrix
• The zero matrix
• The negative of a matrix
• How to determine the equivalence of matrices
• Sums and Differences of matrices
• Additive Identity matrices
• Fundamental properties of matrices
• Symmetric matrices
• Multiplication of a matrix by a scalar
• Properties of scalar multiplication
• Inner products
• The Dot (Scalar) product
• Products of matrices
• Left and Right multiplication
• Conformable matrices
• Matrix multiplication properties