Please enable JavaScript.
Coggle requires JavaScript to display documents.
Chapter 4: System Transient Response, Vectors and Their Types - Coggle…
Chapter 4: System Transient Response
Matrix Types
Matrix Definition
m × n matrix (m rows, n columns)
Special Matrix Types
Null Matrix: All elements are zero.
Diagonal Matrix: Non-diagonal elements are zero.
Identity Matrix: Diagonal elements are all 1.
Partitioned Matrix
Splitting a matrix into smaller components
Matrix Transpose and Symmetry
Matrix Transpose
The transpose of matrix A is formed by swapping rows and columns.
Symmetric Matrix
A matrix aij=aji
Determinants
Minor of an Element
The determinant formed by removing the ith row and the jth column.
Example: For a 3x3 matrix, removing rows and columns around a specific element to compute the minor.
Applications in Systems of Equations
Using Determinants to Solve Systems
Cramer's rule uses determinants to solve systems of linear equations.
Matrix Inversion
The inverse of a matrix A is A^-1 used to solve linear systems
Eigenvalues and Eigenvectors
using the eig(A) function in MATLAB to calculate eigenvalues for system stability analysis
Vectors and Their Types
Row Vector
A matrix with a single row.
Column Vector
A matrix with a single column.
Operations with Vectors
Addition, subtraction, scalar multiplication.