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
Finite dimensional vector spaces over real or complex fields
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)
Lecture 39: Linear Algebra (dimensions of subspaces)
Lecture 40: Linear Algebra (Questions based on the dimension of subspaces)
Linear transformations and their matrix representations
Lecture 41: Linear Algebra (Introduction of Linear Transformation )
Rank and nullity
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
Finite dimensional inner product spaces
Gram-Schmidt orthonormalization process
Definite forms
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