西安建筑科技大学：《线性代数》课程双语教学_教学大纲（英文）.doc_大学文库

(The Difficulty Points) matrix's multiplication; the conception of inverse; Partitioned matrix Depth and Breadth] Understanding the conception of matrix: Mastering matrix's calculator; Knowing partitioned matrix and its calculator Chapter 2 Determinant and Cramer's rule Teaching Content】 The conception of determinant and its properties; Determinant of square matrix's multiplication Adjoint of matrix; The expansion of determinant by row or column; Cramer's rule of linear equation (Teaching request】 1. Understanding determinant; Mastering the properties of determinant; Calculator determinant by properties and the expansion of determinant; Knowing the determinant of square matrixs multiplication 2. Understanding adjoint of matrixs conception; Can solve inverse by adjoint of matrix 3. Knowing Cramer's rule (The Key Points] Determinant's properties and calculator (The Difficulty Points] Determinant's propertie Depth and breadth Understanding determinant; Mastering determinant's properties and calculator Knowing cramer 's rule Chaper 3 Rank of Matrix and solution of Linear Equation Teaching Content】 Elementary operations of matrix; Elementary matrix; equivalent of matrix Rank of matrix; The way to solve the rank of matrix and inverse by elementary operations; Theorem of linear equation has solution Teaching Request】 1. Mastering elementary operations of matrix; Understanding elementary matrix equivalent of matrix and rank of matrix; Mastering the way to solve the rank of matrix and inverse by 2. Understanding full essential condition of homogeneous linear equations has nonzero solution and non-homogeneous linear equations has solution the Key Points] Rank of matrix; The way to solve the rank of matrix and inverse matrix by elementary operations; Equivalent of matrix; Elementary operations and elementary matrix; Theorem of linear equation has solution 【 The Difficulty Points】 Eementary matrix Depth and breadth Mastering inverse matrix and full essential condition of invertible Mastering solve the rank of matrix and inverse matrix by elementary operations Chapter 4 vector and the Structure of Solutions (Teaching content】 Vector space, Linear combination and linear represented of vector; Linear dependence and independence of vectors; The maximal linearly independent collection of vectors; Equal of vector collection; Rank of vector collection The properties and structure of solution The basis for solutions of system and solutions; Solution vector; The way to solve the

【The Difficulty Points】matrix’s multiplication; the conception of inverse ; Partitioned matrix. 【Depth and Breadth】Understanding the conception of matrix; Mastering matrix’s calculator; Knowing partitioned matrix and its calculator. Chapter 2 Determinant and Cramer’s rule 【Teaching Content】 The conception of determinant and its properties; Determinant of square matrix ‘s multiplication; Adjoint of matrix; The expansion of determinant by row or column; Cramer’s rule of linear equation. 【Teaching Request】 1. Understanding determinant; Mastering the properties of determinant; Calculator determinant by properties and the expansion of determinant; Knowing the determinant of square matrix’s multiplication . 2. Understanding adjoint of matrix’s conception; Can solve inverse by adjoint of matrix. 3. Knowing Cramer’s rule. 【The Key Points】Determinant’s properties and calculator. 【The Difficulty Points】Determinant’s properties. 【Depth and breadth】Understanding determinant; Mastering determinant’s properties and calculator; Knowing Cramer’s rule. Chaper 3 Rank of Matrix and Solution of Linear Equation 【Teaching Content】 Elementary operations of matrix; Elementary matrix；equivalent of matrix ；Rank of matrix; The way to solve the rank of matrix and inverse by elementary operations; Theorem of linear equation has solution. 【Teaching Request】 1. Mastering elementary operations of matrix; Understanding elementary matrix 、equivalent of matrix and rank of matrix; Mastering the way to solve the rank of matrix and inverse by elementary operations. 2. Understanding full essential condition of homogeneous linear equations has nonzero solution and non-homogeneous linear equations has solution. 【the Key Points】Rank of matrix; The way to solve the rank of matrix and inverse matrix by elementary operations; Equivalent of matrix; Elementary operations and elementary matrix; Theorem of linear equation has solution) 【The Difficulty Points】Eementary matrix. 【Depth and breadth】Mastering inverse matrix and full essential condition of invertible; Mastering solve the rank of matrix and inverse matrix by elementary operations. Chapter 4 Vector and the Structure of Solutions 【Teaching Content】 Vector space; Linear combination and linear represented of vector; Linear dependence and independence of vectors; The maximal linearly independent collection of vectors; Equal of vector collection; Rank of vector collection ; The properties and structure of solution; The basis for solutions of system and solutions; Solution vector; The way to solve the

solution of linear equations by elementary rows operation Teaching Request】 1. Understanding n-dimension vector; linear combination and linear represented of vectors 2. Understanding the definition of linear dependent and independent of vector collection; Knowing the properties and the way to determine the vector collection are linear dependence or nce 3. Mastering the maximal linearly independent collection of vector and rank of vectors Solve maximal linearly independent collection of vector and the rank of vectors 4. Knowing the conception of vector collections equal Understanding the relations between vector collection's rank and matrixs rank 5. Knowing the conception of n-dimension vector; subspace; basis; dimension 6. Understanding the basis for solutions of system, solutions and solution vector of omogeneous linear equations 7. Understanding the structure of solution and solutions of non-homogeneous linear quations 8. Mastering the way to solve the solution of linear equations by elementary row operation (The Key Points I Linear dependence and independence of vectors; The maximal linearly independent collection and the rank of vectors The way to solve the solution of linear equations by elementary row s operation the Difficulty Points] The conception of vector space; Linear dependence and independence of rectors; Solution space and the basis for solutions of system Depth and breadth I Understanding n-dimension vector; Mastering linear dependence and independence of vectors; Can solve maximal linearly independent collection of vector and he rank of vectors Chapter 5 Eigenvalues Eigenvectors and Quadratic Forms Teaching content】 Eigenvales and eigenvectors of matrix; Inner product; Form linear independence to orthogonal by Gran-Schmidt method; Orthogonal basis; Similar transformation and similar matrix's conception and properties; Full essential condition of diagonalizable and triangular matrix; Quadratic Forms and its matrix form; Rank of Quadratic Forms; Diagonal quadratic fom; Positive definite quadratic forms and positive definite matrices. Teaching Request】 1. Understanding eigenvales and eigenvectors of matrix Can solve eigenvales and eigenvectors 2. Form linear independence to orthogonal by Gram-Schmidt method 3. Understanding similar matrix and knowing full essential condition of diagonalizable 4. Knowing Quadratic Forms and its rank; orthogonal and Positive definite theorem 5. Mastering Quadratic Forms matrix, the way form diagonalizable by orthogonal transformation 6. Knowing quadratic Forms and its matrix's positive definite, Determine of positive definite (The Key Points l Similar matrix; Eigenvales and eigenvector's solution; Diagonalizable of real symmetric matrix; Form diagonalizable by orthogonal transformation. Quadratic Forms and its matrix's positive definite: Determine of positive definite

solution of linear equations by elementary row’s operation. 【Teaching Request】 1. Understanding n-dimension vector; linear combination and linear represented of vectors. 2. Understanding the definition of linear dependent and independent of vector collection; Knowing the properties and the way to determine the vector collection are linear dependence or independence. 3. Mastering the maximal linearly independent collection of vector and rank of vectors; Solve maximal linearly independent collection of vector and the rank of vectors. 4. Knowing the conception of vector collection’s equal ; Understanding the relations between vector collection’s rank and matrix’s rank.. 5..Knowing the conception of n-dimension vector; subspace; basis; dimension. 6. Understanding the basis for solutions of system, solutions and solution vector of homogeneous linear equations. 7. Understanding the structure of solution and solutions of non-homogeneous linear equations. 8. Mastering the way to solve the solution of linear equations by elementary row’s operation. 【The Key Points】Linear dependence and independence of vectors; The maximal linearly independent collection and the rank of vectors; The way to solve the solution of linear equations by elementary row’s operation . 【the Difficulty Points】The conception of vector space; Linear dependence and independence of vectors; Solution space and the basis for solutions of system. 【Depth and breadth】Understanding n-dimension vector; Mastering linear dependence and independence of vectors; Can solve maximal linearly independent collection of vector and the rank of vectors. Chapter 5 Eigenvalues 、Eigenvectors and Quadratic Forms 【Teaching Content】 Eigenvales and eigenvectors of matrix; Inner product; Form linear independence to orthogonal by Gran-Schmidt method; Orthogonal basis; Similar transformation and similar matrix’s conception and properties; Full essential condition of diagonalizable and triangular matrix; Quadratic Forms and its matrix form; Rank of Quadratic Forms; Diagonal quadratic form; Positive definite quadratic forms and positive definite matrices.）【Teaching Request】 1. Understanding eigenvales and eigenvectors of matrix; Can solve eigenvales and eigenvectors of matrix;) 2．Form linear independence to orthogonal by Gram-Schmidt method. 3. Understanding similar matrix and knowing full essential condition of diagonalizable. 4. Knowing Quadratic Forms and its rank; orthogonal and Positive definite theorem. 5. Mastering Quadratic Forms matrix ,the way form diagonalizable by orthogonal transformation. 6. Knowing quadratic Forms and its matrix ‘s positive definite, Determine of positive definite. 【The Key Points】Similar matrix; Eigenvales and eigenvector’s solution; Diagonalizable of real symmetric matrix; Form diagonalizable by orthogonal transformation. Quadratic Forms and its matrix ‘s positive definite; Determine of positive definite