linear algebra
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
Vector spaces
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 )
Vector subspaces
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 )
Linear dependence
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)
Basis and dimension
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
Algebra of linear transformations
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)
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 )
Algebra of matrices
Matrix Algebra | Lecture 1| Linear Algebra | Mathematics | CSIR UGC NET
Matrix Algebra | Lect 2 | Linear Algebra | Mathematics
Rank and determinant of matrices
Linear equations
Eigenvalues and eigenvectors
Cayley-Hamilton theorem
Matrix representation of 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?)
Change of basis
Canonical forms
Diagonal forms
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. )
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 )
Triangular forms
Jordan forms
Inner product spaces
Orthonormal basis
Quadratic forms
Reduction and classification of quadratic forms
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