Properties and evaluation techniques, including symmetric and skew-symmetric determinants. Vector Spaces: Study of vectors in cap R to the n-th power cap C to the n-th power spaces, linear independence, and spanning sets. Linear Transformations: Mathematical mapping between vector spaces. Eigenvalues and Eigenvectors:
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A set $V$ is a vector space if, under operations of addition and scalar multiplication, it satisfies 10 axioms (closure, associativity, commutativity, existence of zero vector, existence of additive inverse, etc.). Properties and evaluation techniques