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noc20-ma54-lec24 - Basic Results on Linear Independence
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Classroom Contents
Linear Algebra
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- 1 Intro - Linear Algebra
- 2 noc20-ma54-lec01_Notations, Motivation and Definition
- 3 noc20-ma54-lec02_Matrix: Examples, Transpose and Addition
- 4 noc20-ma54-lec03_Matrix Multiplication
- 5 noc20-ma54-lec04_Matrix Product Recalled
- 6 noc20-ma54-lec05_Matrix Product Continued
- 7 noc20-ma54-lec06_Inverse of a Matrix
- 8 noc20-ma54-lec07 - Introduction to System of Linear Equations
- 9 noc20-ma54-lec08 - Some Initial Results on Linear Systems
- 10 noc20-ma54-lec09 - Row Echelon Form (REF)
- 11 noc20-ma54-lec10 - LU Decomposition - Simplest Form
- 12 noc20-ma54-lec11 - Elementary Matrices
- 13 noc20-ma54-lec12 - Row Reduced Echelon Form (RREF)
- 14 noc20-ma54-lec13 - Row Reduced Echelon Form (RREF) Continued
- 15 noc20-ma54-lec14 - RREF and Inverse
- 16 noc20-ma54-lec15 - Rank of a matrix
- 17 noc20-ma54-lec16 - Solution Set of a System of Linear Equations
- 18 noc20-ma54-lec17 - System of n Linear Equations in n Unknowns
- 19 noc20-ma54-lec18 - Determinant
- 20 noc20-ma54-lec19 - Permutations and the Inverse of a Matrix
- 21 noc20-ma54-lec20 - Inverse and the Cramer's Rule
- 22 noc20-ma54-lec21 - Vector Spaces
- 23 noc20-ma54-lec22 - Vector Subspaces and Linear Span
- 24 noc20-ma54-lec23 - Linear Combination, Linear Independence and Dependence
- 25 noc20-ma54-lec24 - Basic Results on Linear Independence
- 26 noc20-ma54-lec25 - Results on Linear Independence Continued...
- 27 noc20-ma54-lec26 - Basis of a Finite Dimensional Vector Space
- 28 noc20-ma54-lec27 - Fundamental Spaces associated with a Matrix
- 29 noc20-ma54-lec28 - Rank - Nullity Theorem
- 30 noc20-ma54-lec29 - Fundamental Theorem of Linear Algebra
- 31 noc20-ma54-lec30 - Definition and Examples of Linear Transformations
- 32 noc20-ma54-lec31 - Results on Linear Transformations
- 33 noc20-ma54-lec32 - Rank-Nullity Theorem and Applications
- 34 noc20-ma54-lec33 - Isomorphism of Vector Spaces
- 35 noc20-ma54-lec34 - Ordered Basis of a Finite Dimensional Vector Space
- 36 noc20-ma54-lec35 - Ordered Basis Continued
- 37 noc20-ma54-lec36 - Matrix of a Linear transformation
- 38 noc20-ma54-lec37 - Matrix of a Linear transformation Continued...
- 39 noc20-ma54-lec38 - Matrix of Linear Transformations Continued...
- 40 noc20-ma54-lec40 -Inner Product Space
- 41 noc20-ma54-lec41 - Inner Product Continued
- 42 noc20-ma54-lec42 - Cauchy Schwartz Inequality
- 43 noc20-ma54-lec43 - Projection on a Vector
- 44 noc20-ma54-lec44 - Results on Orthogonality
- 45 noc20-ma54-lec45 - Results on Orthogonality
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