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Linear Algebra (Core concepts) (Special Matrices (Orthogonal Matrix (The…
Linear Algebra
(Core concepts)
Solving Linera Systems
Gaussian Elimination
Row Echelon Form (REF)
Reduced Row Echelon Form (RREF)
Pivots
Free Variables
Augmented Matrix
Elementary Row Operations
Type 1: Switching Row
Type 2: Scaling Row
Type 3: Adding Row
Matrix
Decomposition
LU Decomposition
(A=LU or A=LUP)
Lower Triangular Matrix (REF)
Upper Triangular Matrix
QR Decomposition
Eigen Decomposition
(A=QΛQᵀ)
EigenVector
EigenValue
EigenBasis
Singular Value Decomposition
(A=UΣVᵀ)
Cholesky Decomposition
(A=LLᵀ or A=UᵀU)
Special Matrices
Identity Matrix
Permutation Matrix (Switching Rows of Identity Matrix)
Transpose (Flipping entries about diagonal)
Symmetric Matrix (Symmetric entries alone diagonal)
Square Matrix
Triangular Matrix
Orthogonal Matrix
The Gram–Schmidt process
Orthonormal Basis
Sparse Matrix (Most entries are 0)
Elementary Matrix (One Elementary Row Operation)
Vector Space | Subspace
Column Space
Null Space
Vector Projection
Change of Basis
Vector Norms
Matrix Multiplication
Entries Method
Row Method
Column Method
Column Row Method
Inverse of Matrices
Gaussian Elimination Method
Cramer's Rule Method
(Determinant/Adjugates)