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Lec19 Existence of a basis
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Classroom Contents
Linear Algebra
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- 1 Lec01 Introduction to Algebraic Structures Rings and Fields
- 2 Lec02 Defnition of Vector Spaces
- 3 Lec03 Examples of Vector Spaces
- 4 lec04 Defnition of subspaces
- 5 Lec05 Examples of subspaces
- 6 Lec06 Examples of subspaces continued
- 7 Lec07 Sum of subspaces
- 8 Lec08 System of linear equations
- 9 lec09 Gauss elimination
- 10 Lec10 Generating system , linear independence and bases
- 11 Lec11 Examples of a basis of a vector space
- 12 Lec12 Review of univariate polynomials
- 13 Lec13 Examples of univariate polynomials and rational functions
- 14 Lec14 More examples of a basis of vector spaces
- 15 Lec15 Vector spaces with finite generating system
- 16 Lec16 Steinitzs exchange theorem and examples
- 17 Lec17 Examples of finite dimensional vector spaces
- 18 Lec18 Dimension formula and its examples
- 19 Lec19 Existence of a basis
- 20 Lec20 Existence of a basis continued
- 21 Lec21 Existence of a basis continued
- 22 Lec22 Introduction to Linear Maps
- 23 Lec23 Examples of Linear Maps
- 24 Lec24 Linear Maps and Bases
- 25 Lec25 Pigeonhole principle in Linear Algebra
- 26 Lec26 Interpolation and the rank theorem
- 27 Lec27 Examples
- 28 Lec28 Direct sums of vector spaces
- 29 Lec29 Projections
- 30 Lec30 Direct sum decomposition of a vector space
- 31 Lec31 Dimension equality and examples
- 32 Lec32 Dual spaces
- 33 Lec33 Dual spaces continued
- 34 Lec34 Quotient spaces
- 35 Lec35 Homomorphism theorem of vector spaces
- 36 Lec36 Isomorphism theorem of vector spaces
- 37 Lec37 Matrix of a linear map
- 38 Lec38 Matrix of a linear map continued
- 39 Lec39 Matrix of a linear map continued
- 40 Lec40 Change of bases
- 41 Lec41 Computational rules for matrices
- 42 Lec42 Rank of a matrix
- 43 Lec43 Computation of the rank of a matrix
- 44 Lec44 Elementary matrices
- 45 Lec45 Elementary operations on matrices
- 46 Lec46 LR decomposition
- 47 Lec47 Elementary Divisor Theorem
- 48 Lec48 Permutation groups
- 49 Lec49 Canonical cycle decomposition of permutations
- 50 Lec50 Signature of a permutation
- 51 Lec51 Introduction to multilinear maps
- 52 Lec52 Multilinear maps continued
- 53 Lec53 Introduction to determinants
- 54 Lec54 Determinants continued
- 55 Lec55 Computational rules for determinants
- 56 Lec56 Properties of determinants and adjoint of a matrix
- 57 Lec57 Adjoint determinant theorem
- 58 Lec58 The determinant of a linear operator
- 59 Lec59 Determinants and Volumes
- 60 Lec60 Determinants and Volumes continued
