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advanced-linear-algebra

Dual bases

taught

Given a basis of V, the dual basis of V* satisfies phi_i(b_j) = delta_ij -- existence and uniqueness, proved.

Taught in

Dual bases
Advanced Linear Algebra

Requires

the-dual-space required
the-exchange-lemma required

Required by

Coordinates are functionals required
Orthonormal bases and Fourier coefficients required
The double dual and natural vs. non-natural isomorphism required
The matrix of the dual map is the transpose required

Local knowledge map

Local knowledge map

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Solid arrows are required prerequisites; dashed are recommended or helpful. Lower rows are more foundational. Click any box to jump to that concept.