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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
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 )
Linear independence of vectors
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, 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
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)
Matrix representation
Range space
Null space
Rank-nullity theorem
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 73: Linear Algebra ( Interesting examples of change of basis matrices )
Rank and inverse of a matrix
Determinant
Matrix Algebra | Lecture 1| Linear Algebra | Mathematics | CSIR UGC NET
Matrix Algebra | Lect 2 | Linear Algebra | Mathematics
Matrix Algebra Lecture 3 | Transpose Of a matrix | Linear Algebra
Matrix Algebra | Lecture 4 | Trace of a matrix | CSIR UGC NET
Matrix Algebra | Lecture 5 | CSIR UGC NET | Rank of the matrix | Properties
Matrix Algebra || Lecture 6 || System Of Linear Equations
MATRIX ALGEBRA || LECTURE 7
Matrix Algebra || Lecture 8 || TRICKS TO CALCULATE EIGEN VALUE
MATRIX ALGEBRA || LECTURE 9 || FINDING EIGEN VALUES USING CONCEPT OF BLOCK MATRIX
#Lecture10 || How to calculate Algebraic Multiplicity and Geometric Multiplicity || Matrix Algebra
Solutions of systems of linear equations
Consistency conditions
Eigenvalues and eigenvectors for matrices
Eigen values and Eigen vectors
Row reduced Echelon form
Questions on Row reduced Echelon form and Row Echelon form
Rank of a matrix
System of equations
System of equations continued
Finding inverse of a matrix using row transformations
Cayley-Hamilton theorem
Please note: Cayley-Hamilton theorem would be covered soon.
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