MathIsimple
Part IV

Matrix Theory

Matrices are the computational backbone of linear algebra. They represent linear maps concretely, enabling explicit calculations.

6
Courses
14-19
Hours
Core
Level

Courses

LA-4.1
Matrix Representation
Available
Representing linear maps as matrices with respect to bases
3-4 hours
Coordinate Vectors
Matrix of Linear Map
Change of Basis
LA-4.2
Matrix Operations
Available
Addition, scalar multiplication, matrix multiplication, and transpose
2-3 hours
Matrix Arithmetic
Multiplication
Transpose
Block Matrices
LA-4.3
Matrix Inverse
Available
Invertible matrices, computing inverses, and characterizations
2-3 hours
Inverse Definition
Computing Inverse
Invertibility Criteria
LA-4.4
Elementary Matrices
Available
Elementary row operations as matrix multiplication
2-3 hours
Three Types
LU Decomposition
Row Reduction
LA-4.5
Rank & Equivalence
Available
Row rank, column rank, and matrix equivalence
2-3 hours
Row/Column Rank
Rank = Row Rank = Column Rank
Equivalence
LA-4.6
Special Matrices
Available
Symmetric, orthogonal, triangular, and other special matrices
2-3 hours
Symmetric
Orthogonal
Triangular
Diagonal