Linear Algebra
( 24 Module )

module #1
Introduction to Linear Algebra
Overview ng kurso, kahalagahan ng linear algebra, at basic concepts

module #2
Vector Operations
Addition, scalar multiplication, at basic properties ng vectors

module #3
Vector Spaces
Kahulugan, mga halimbawa, at katangian ng mga vector space

module #4
Subspaces
Definition, mga halimbawa, at katangian ng mga subspaces

module #5
Span at Basis
Span ng isang set ng mga vectors, batayan ng isang vector space, and basis theorems

module #6
Linear Independence
Definition, examples, and tests for linear independence

module #7
Dimension and Rank
Dimension of a vector space, rank of a matrix, and relationships between them

module #8
Matrix Operations
Addition, scalar multiplication, at matrix multiplication

module #9
Inverse and Determinant of a Matrix
Definition, properties, at kalkulasyon ng inverse at determinant ng isang matrix

module #10
Linear Transformations
Definition, halimbawa, at katangian ng linear transformations

module #11
Matrix Representations of Linear Transformations
Matrix representation of linear transformations at ang kanilang mga katangian

module #12
Eigenvalues and Eigenvectors
Definition, kalkulasyon, at mga katangian ng eigenvalues at eigenvectors

module #13
Diagonalization ng Matrices
Diagonalization ng mga matrice, diagonalization, at mga application

module #14
Orthogonality at Orthonormality
Orthogonal at orthonormal vectors, Gram-Schmidt na proseso, at orthogonal projection

module #15
Orthogonal Matrices at QR Decomposition
Orthogonal matrice, QR decomposition, at mga application

module #16
Linear Systems and Row Operations
Linear system, row operations, at solving system gamit ang Gaussian elimination

module #17
Null Space at Column Space
Null space at column space ng isang matrix, at mga relasyon sa pagitan ng mga ito

module #18
Image at Kernel
Image at kernel ng isang linear transformation, at mga relasyon sa pagitan ng mga ito

module #19
Singular Value Decomposition (SVD)
Definition, properties, at applications ng SVD

module #20
Markov Chains and PageRank
Introduction to Markov chains, PageRank algorithm, at applications

module #21
Computer Graphics and Linear Algebra
Mga application ng linear algebra sa computer graphics

module #22
Machine Learning at Linear Algebra
Applications ng linear algebra sa machine learning

module #23
Statistics at Linear Algebra
Applications ng linear algebra sa statistics

module #24
Pagtatapos ng Kurso at Konklusyon
Pagpaplano ng mga susunod na hakbang sa Linear Algebra career

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