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Good Books for reference:
Good Books for reference:
Schaum's Outline of Linear Algebra
Linear algebra done right (S. Axler)
An Introduction to Linear Algebra (Gilbert Strang)
Syllabus for linear algebra
Syllabus for linear algebra
Finite dimensional vector spaces over real or complex fields
Lecture 1: Linear Algebra ( what is a FIELD ?)
Lecture 2: Linear Algebra (What are Vector Spaces?)
Lecture 3: Linear Algebra ( Examples of Vector spaces.)
Lecture 4: Linear Algebra ( Examples of vector spaces.)
Lecture 5: Linear Algebra ( Examples of vector spaces. )
Lecture 6: Linear Algebra ( Linear combinations of vector spaces. )
Lecture 7: Linear Algebra ( Question based on linear combination of vectors.)
Lecture 8: Linear Algebra ( Span of vectors u1, u2, ........ , um)
Lecture 9: Linear Algebra ( Spanning set of a vector space. )
Lecture 10: Linear Algebra ( Result on spanning sets. )
Lecture 11: Linear Algebra (Result on spanning set)
Lecture 12: Linear Algebra ( result on spanning sets.)
Lecture 13: Linear Algebra ( Examples of spanning sets of vector spaces )
Lecture 14: Linear Algebra ( Vector subspaces. )
Lecture 15: Linear Algebra ( Examples of vector subspaces. )
Lecture 16: Linear Algebra ( Examples of subspaces. )
Lecture 17: Linear Algebra ( An essential theorem for vector subspaces.)
Lecture 18: Linear Algebra ( Trivial and non trivial subspaces. )
Lecture 19: Linear Algebra ( Span of a subset is a subspace.)
Lecture 20: Linear Algebra ( span of a subset S is the smallest subspace containing S)
Lecture 21: Linear Algebra ( intersection of subspaces )
Lecture 22: Linear Algebra ( Questions on intersection of subspaces)
Lecture 23: Linear Algebra ( Questions on intersection of subspaces.)
Lecture 24: Linear Algebra ( union and sum of vector subspaces. )
Lecture 25: Linear Algebra ( Sum and union of vector spaces. )
Lecture 26: Linear Algebra ( Direct sum of vector subspaces )
Lecture 27: Linear Algebra ( Necessary and sufficient condition for direct sum of vector spaces )
Lecture 28: Linear Algebra ( question based on direct sum of vector spaces )
Lecture 29: Linear algebra (Linearly independent and dependent sets.)
Lecture 30: Linear algebra ( geometrical interpretation of Linearly dependent vectors )
Lecture 31: Linear Algebra ( Some basic results on Linearly dependent vectors )
Lecture 32: Linear algebra ( Some results on linearly dependent vectors)
Lecture 33: Linear Algebra ( Basis of a vector space ).
Lecture 34: Linear algebra ( Some results on basis of a vector space)
Lecture 35: Linear Algebra (dimension of a vector space)
Lecture 36: Linear Algebra (Equivalent definition of a basis)
Lecture 37: Linear Algebra (Coordinate vectors)
Lecture 38: Linear Algebra (Any linearly independent set can be extended to a basis) Download pdf Lecture 38
Lecture 39: Linear Algebra (dimensions of subspaces)
Lecture 40: Linear Algebra (Questions based on the dimension of
subspaces) Download pdf Lecture 40
Linear transformations and their matrix representations
Lecture 41: Linear Algebra (Introduction of Linear Transformation )
Lecture 42: Linear Algebra ( Examples of Linear transformations)
Lecture 43: Linear Algebra ( Multiplication with a matrix is a linear transformation)
Lecture 44: Linear Algebra (Rotation is a linear Transformation)
Lecture 45: Linear Algebra ( Properties of linear Transformation)
Lecture 46: Linear Algebra ( Construction of linear transformations)
Rank and nullity
Lecture 47: Linear Algebra ( Range and Null space of a Linear transformation )
Lecture 48: Linear Algebra ( Examples of null spaces and range of different linear transformations )
Lecture 49: Linear Algebra ( Some more properties of linear transformations)
Lecture 50: Linear Algebra ( Linear independence is preserved or not under a linear transformation )
Lecture 51: Linear Algebra ( Rank Nullity Theorem )
Lecture 52: Linear Algebra (Verification of rank Nullity theorem )
Lecture 53: Linear Algebra ( Isomorphisms )
Lecture 54: Linear Algebra ( Inverse of a non singular linear map is linear and non singular )
Lecture 55: Linear Algebra (transformations which are either one one or onto )
Lecture 56: Linear Algebra (Finding the inverse of an isomorphism )
Lecture 57: Linear Algebra (Isomorphic vector spaces. )
Lecture 58: Linear Algebra ( set of all linear transformations from U to V forms a vector space )
Lecture 59: Linear Algebra (Composition/Product of linear transformations )
Lecture 60: Linear Algebra ( Some more results on linear transformations )
Lecture 61: Linear Algebra ( Matrix representations of linear transformations )
Lecture 62: Linear Algebra ( Examples of matrix representations of linear transformations )
Lecture 63: Linear Algebra (More examples of matrix representations of linear transformations )
Lecture 64: Linear Algebra ( matrix representation of T to compute coordinate vector of T(v))
Lecture 65: Linear Algebra ( Isomorphism of the linear transformations and space of matrices )
Lecture 66: Linear Algebra ( Conversion of units equivalence to matrix representation of linear maps)
Lecture 67: Linear Algebra ( Interesting example from a car factory )
Lecture 68: Linear Algebra ( Matrix representations of sum, scalar multiple and composition of LTs)
Lecture 69: Linear Algebra ( Interesting example of composition of linear transformations)
Lecture 70: Linear Algebra ( Why linear transformations are not same as matrices?)
Lecture 71: Linear Algebra ( Change of basis matrix )
Lecture 72: Linear Algebra ( Change of basis matrix examples )
Lecture 73: Linear Algebra ( Interesting examples of change of basis matrices )
Lecture 74: Linear Algebra ( Change of basis and matrices of linear transformations )
Lecture 75: Linear Algebra ( Why we need the diagonalization of linear operators )
Lecture 76: Linear Algebra ( Defining Eigenvalues and Eigenvectors of a linear operator. )
Systems of linear equations
Eigenvalues and eigenvectors
Minimal polynomial
Cayley-Hamilton Theorem
Diagonalization
Jordan canonical form
Symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal and unitary matrices
Lecture 77: Linear Algebra ( Eigen space of c is same as null space of T-cI )
Lecture 78: Linear Algebra ( Computing the Eigen values and Eigen vectors of a linear operator )
Lecture 79: Linear Algebra ( Examples of finding the Eigen values and Eigen vectors of LTs )
Lecture 80: Linear Algebra ( Diagonalizable linear operators )
Lecture 81: Linear Algebra (Algorithm to check if a given linear operator is Diagonalizable )
Lecture 82: Linear Algebra ( Examples of diagonalization of linear operators )
Lecture 83: Linear Algebra ( Eigenvectors corresponding to distinct Eigenvalues are LI )
Lecture 84: Linear Algebra ( Test for diagonalizability when all the Eigenvalues are not distinct. )
Lecture 85: Linear Algebra ( diagonalizing linear operators when Eigen values are not distinct)
Lecture 86: Linear Algebra ( All the Eigenvalues of a real symmetric matrix are always real)
Lecture 87: Linear Algebra ( A real symmetric matrix is orthogonally diagonalizable )
Lecture 88 Linear Algebra (A diagonalizable nilpotent matrix is a zero matrix)
Lecture 89 Linear Algebra (The Caley Hamilton Theorem)
Lecture 90 Linear Algebra (Minimal polynomial of a square matrix)
Lecture 91 Linear Algebra (Same irreducible factors of Minimal and characterstic polynomials)
Lecture 92 Linear Algebra (How to find the minimal polynomial of a square matrix)
Lecture 93 Linear Algebra (Examples of finding minimal polynomials)
Lecture 94 Linear Algebra (Minimal polynomial of a linear transformation)
Lecture 95 Linear Algebra (Characterstic polynomial of a block triangular and diagonal matrix)
Lecture 96 Linear Algebra (Minimal Polynomial of a block diagonal matrix)
Lecture 97 Linear Algebra (Finding minimal polynomials of block diagonal matrix)
Lecture 98 Linear Algebra (Invariant Subspaces)
Lecture 99 Linear Algebra (1d invariant subspaces)
Lecture 100 Linear Algebra (Results on invariant subspace)
Lecture 101 Linear Algebra (Results on invariant subspaces)
Lecture 102 Linear Algebra (Trivial invariant subspaces)
Lecture 103 Linear Algebra (Intersection of T invariant subspaces is T invariant)
Lecture 104 Linear Algebra (Problems on invariant subspaces)
Lecture 105 Linear Algebra (Direct Sum decomposition)
Lecture 106 Linear Algebra (Direct Sum Decomposition Theorem)
Lecture 107 Linear Algebra (T invariant Direct Sum Decomposition)
Lecture 108 Linear Algebra (Representation of T when V has invariant direct sum decomposition)
Lecture 109 Linear Algebra (Primary Decomposition Theorem I)
Lecture 110 Linear Algebra (Primary decomposition Theorem II)
Lecture 111 (Linear Algebra Primary Decomposition Theorem III)
Lecture 112 Linear Algebra (Application of Primary Decomposition Theorem)
Lecture 113 Linear Algebra (Question of diagonalization of a linear operator)
Lecture114 Linear Algebra (Nilpotent Operators)
Lecture 115 Linear Algebra Results on Nilpotent Operators I
Lecture 116 Linear Algebra Results on Nilpotent Operators II
Lecture 117 Linear Algebra Results on Nilpotent Operators III
Lecture 118 Linear Algebra Matrix Representation of Nilpotent Operators
Lecture 119 Linear Algebra Matrix Representation of Nilpotent Operator Questions
Finite dimensional inner product spaces
Live Stream: Introduction to Inner Product Spaces
Inner product spaces and Cauchy Schwarz Inequality
Gram-Schmidt orthonormalization process
Definite forms
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