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 over R and C, Subspaces
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 dependence and independence
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)
Lecture 39: Linear Algebra (dimensions of subspaces)
Lecture 40: Linear Algebra (Questions based on the dimension of subspaces)
Linear transformations
Lecture 41: Linear Algebra (Introduction of Linear Transformation )
Rank and nullity
Matrix of a linear transformation
Algebra of Matrices
Row and column reduction
Echelon form
Congruence’s and similarity
Rank of a matrix
Inverse of a matrix
Solution of system of linear equations
Eigenvalues and eigenvectors
Characteristic polynomial
Cayley-Hamilton theorem
Symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal and unitary matrices and their eigenvalues
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