TAILIEUCHUNG - Lecture Linear algebra: Chapter 5 - TS. Đặng Văn Vinh

Lecture "Linear algebra - Chapter 5: Linear transformation" provides learners with the knowledge: Definition and examples, the Kernel and Image of linear transformation, the Matrix of a linear transformation, the Matrix of a linear transformation, similarity. Invite you to refer to the disclosures. | Math Dept Faculty of Applied Science HCM University of Technology Subject Linear Algebra Chapter 5 Linear transformation Instructor Dr. Dang Van Vinh 12 2006 CONTENTS I - Definition and examples II - The Kernel and Image of linear transformation III - The Matrix of a linear transformation IV -Transition Matrix and change of basis V -Similarity I. The Definition and Examples Definition of mapping Transformation Given two sets X and Y if we assign to each element x of X one and only one element y of Y then the rule of assignment is called a function or a mapping or a transformation . f X T Y x f x y The set X is called the domain of the function f. The set Y is called the co-domain of the function f. For an element x of the domain the assigned element f x is called the image of x. The set of all images which is a subset of the co-domain Y is called the range of the .

• Toán học
• Lecture Linear algebra
• Linear transformation
• Definition and examples
• Image of linear transformation
• The Matrix of a linear transformation
• The Matrix of a linear transformation
• Systems of linear equations
• Lecture Systems of linear equations
• Homogeneous system
• Lecture Homogeneous system
• Lecture Matrix Algebra
• Elementary row operations
• Matrix operations
• A rank of matrix
• An inverse of matrix
• Eigenvalues and Eigenvectors
• Eigenvectors and linear transformations
• Hermitian matrices
• Quadratic form
• Linear transformations
• Vector space
• Lecture Vector space
• Linear independence
• Rank of vectors
• Basic and dimension
• Lecture Notes on Linear System Theory
• Linear system theory
• Introduction to Algebra
• Introduction to Analysis
• Time varying linear systems
• Time invariant linear systems
• Coordinates of a vector
• The intersection
• Sum of subspaces
• The standard form
• The trigonometric form
• The exponential form
• The Power of complex numbers
• The Roots of complex numbers
• The Orthogonality and Least Squares
• The Scalar Product in R
• Orthogonal subspaces
• Orthonormal set
• The gram schmidt orthogonalization process
• Lecture Mathematics
• Lecture Determinant
• The determinant of matrix
• Properties of determinant
• Laplace’s expansion
• Lecture laplace’s expansion
• Lecture Calculus
• Bài giảng Giải tích
• Velocity and tangents
• Linear Algebra
• Differential Geometry
• mathematics
• scalar
• vector
• duality
• normality