33
Matrix Operations
| Date post: | 20-Dec-2015 |
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Matrix Operations
Matrix Notation
Example
Equality of Matrices
Square Matrix
Diagonal Matrix
Triangular Matrices
Row and Column Vectors
Transposition of Vectors
Transposition of Matrices
Example
Symmetric and Skew-Symmetric Matrices
Addition of Matrices
Scalar Multiplication
Zero Matrix
Properties of Additon
Properties of Scalar Multiplication
Properties of Tranposition
Product of Matricies
Product of Matricies
Identity Matrices
Identity Property
A System of Linear Equations
The Matrix Equation Ax=b
Properties of Matrix Multiplication
Cautions
Matrix Powers
Theorem
Properties of Transposition
Definition of Linear Combination
Consistency Theorem for Linear Systems
A linear system Ax=b is consistent if and only if b can be written as a linear combination of the column vectors of A.
Definition
Matrix Inverse Identities
![Section 3.1 The Determinant of a Matrix. Determinants are computed only on square matrices. Notation: det(A) or |A| For 1 x 1 matrices: det( [k] ) = k.](https://static.documents.pub/doc/80x56/56649d015503460f949d3eab/section-31-the-determinant-of-a-matrix-determinants-are-computed-only-on.jpg)
