Linear Algebra: Syllabus
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Vector spaces over and
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Linear dependence and independence
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Subspaces
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Bases
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Dimensions
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Linear transformations
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Rank and nullity
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Matrix of a linear transformation
- Algebra of Matrices
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Row and column reduction
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Echelon form
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Congruence and similarity
- Rank of a matrix
- Inverse of a matrix
- Solution of system of linear equations
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Eigenvalues and eigenvectors
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Characteristic polynomial
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Cayley-Hamilton theorem
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Symmetric, skew-symmetric, Hermitian, orthogonal and unitary matrices and their eigenvalues