MindMap Gallery linear algebra
This is a mind map about linear algebra, mainly including vector space, eigenvalues and eigenvectors, orthogonality and least squares method, determinant of square matrices, etc.
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The ice hockey schedule for the Milano Cortina 2026 Winter Olympics, featuring preliminary rounds, quarterfinals, and medal matches for both men's and women's tournaments from February 5–22. All game times are listed in Eastern Standard Time (EST).
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This Valentine's Day map illustrates love through 30 romantic possibilities, from the vintage charm of "handwritten love letters" to the urban landscape of "rooftop sunsets," from the tactile experience of a "pottery workshop" to the leisurely moments of "wine tasting at a vineyard"—offering a unique sense of occasion for every couple. Whether it's cozy, experiential, or luxurious, love always finds the most fitting expression. May you all find the perfect atmosphere for your love story.
The ice hockey schedule for the Milano Cortina 2026 Winter Olympics, featuring preliminary rounds, quarterfinals, and medal matches for both men's and women's tournaments from February 5–22. All game times are listed in Eastern Standard Time (EST).
linear algebra
vector space
vector definition
Vector representation
Coordinate representation
Vector operations
Addition of vectors
Subtraction of vectors
Multiplication of vectors
vector product of vectors
Linear dependence of vectors
linearly independent vector group
Linearly related vector groups
matrix
matrix definition
Representation method of matrix
row matrix
column matrix
diagonal matrix
Identity matrix
zero matrix
Matrix operations
Addition of matrices
Subtraction of matrices
Multiplication of matrices
Matrix multiplication
transpose of matrix
inverse of matrix
Rank of the matrix
Definition of rank of matrix
Calculation of the rank of a matrix
System of linear equations
Definition of a system of linear equations
How to express a system of linear equations
matrix form
vector form
Solutions to systems of linear equations
Conditions for a system of linear equations to have solutions
Necessary and sufficient conditions for a system of linear equations to have solutions
Properties of solutions to systems of linear equations
Uniqueness of solutions to linear equations
Stability of solutions to linear equations
Solution to a system of linear equations
Gaussian elimination method
Matrix inversion
Clem's Law
Eigenvalues and eigenvectors
Definition of eigenvalues and eigenvectors
Definition of eigenvalues
Definition of feature vector
Calculation of eigenvalues and eigenvectors
Calculation of eigenvalues
properties of eigenvalues
How to calculate eigenvalues
Calculation of eigenvectors
Properties of eigenvectors
How to calculate eigenvectors
Application of eigenvalues and eigenvectors
matrix diagonalization
Definition of matrix diagonalization
Matrix diagonalization method
Quadratic type
Definition of quadratic form
Standard type of quadratic type
Positive definiteness of quadratic form
Orthogonality and least squares
Definition of orthogonality
orthogonal vector
Orthogonal matrix
Definition of least squares method
The basic idea of the least squares method
Solving method using least squares method
Solution of least squares method
direct solution
indirect solution
Application of least squares method
linear regression
Definition of linear regression
How to solve linear regression
Least squares method to solve linear regression
Gradient descent method to solve linear regression
Curve Fitting
Curve fitting definition
Curve fitting solution method
Least squares method to solve curve fitting
Gradient descent method solves curve fitting;
determinant of square matrix
concepts and definitions
The determinant is a linear algebra operation used to describe a square matrix
Determinant represents the linear transformation of a square matrix
The determinant can represent the rank and eigenvalues of a square matrix
Calculation method
Calculate using the properties of determinants
Calculate using determinant expansion theorem
Calculate using the inverse matrix of the determinant
Determinant properties
The determinant is related to the transpose operation of the matrix
Determinants are related to elementary transformations of matrices
The determinant is related to the rank of the matrix
The determinant is related to the eigenvalues of the matrix
Applications of determinants
Solve a system of linear equations
Calculate the rank of a matrix
Calculate the eigenvalues of a matrix
Compute the inverse of a matrix
Limitations of determinants
Determinants only apply to square matrices
Determinant calculation is complex and error-prone
Determinants tend to lose precision during calculations
Summarize
Determinant is an important linear algebra operation
Determinants are widely used in matrix operations and linear transformations
Determinant calculation requires mastering certain skills and methods to avoid errors and loss of accuracy.
Vector spaces and the structure of solutions to linear equations
Basic concepts of vector space
vector definition
Vector representation
Coordinate representation
geometric representation
Vector operations
Addition of vectors
Subtraction of vectors
Multiplication of vectors
vector product of vectors
Properties of vector spaces
Linear dependence and linear independence
Definition of linear correlation
The definition of linear independence
Judgment method of linear correlation
Dimension of vector space
Definition of dimension
How to calculate dimensions
Basic concepts of linear equations
Definition of a system of linear equations
General form of linear equations
Special forms of systems of linear equations
Solutions to systems of linear equations
solution definition
properties of solutions
How to find the solution
Structural relationship between vector space and solutions to linear equations
The connection between vector space and linear equations
Correspondence between vectors in vector space and unknown quantities in a system of linear equations
Structure of solutions to systems of linear equations
Vector space representation of solutions to linear equations
Bases and dimensions of vector spaces
Vector space representation of solutions to linear equations
Structural Theorem of Solutions to Linear Equations
Contents of the structure theorem of solutions to linear equations
Proof of the Structure Theorem of Solutions to Linear Equations
Applications of Solutions to Linear Equations
Application of solutions to linear equations in engineering problems
Application of solutions to linear equations in structural analysis
Application of solutions to linear equations in control systems
Application of solutions to linear equations in scientific research
Applications of solutions to linear equations in physics
Applications of solutions to linear equations in chemistry;