Summary
Inverse of 2x2 matrix, with 2x2 determinant
Algorithm to find the inverse
if
has zero rows it means that some dimension are lost
Cancellation law for invertible matrices
note: the order of multiplication due to non-commutativity
Rules
similar to transpose
Equivalent statements of invertibility
Concept
All non-square matrices are non-invertible
- due to the non-commutativity of matrix multiplication
Invertible square matrix
singular matrix is a non-invertible square matrix
Rationale for inverse, solving linear systems
Negative power of invertible matrices
Uniqueness of inverse
Cancellation law
Inverse of symmetric matrix is also symmetric
Inverse of matrix product
Application
Homogeneous system with invertible coefficient matrix
Computing the inverse of a 2x2 matrix
Extra
Compiled equivalent statements of invertibility
Extra
Octave
octave
# Inverse of a matrix, if it exists
inv(A)