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Linear Algebra and Representation Theory
Linear Algebra and Representation Theory
foundations +49 more results +55 more equations +31 more depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) definition 5.1: Double factorial 5.1 Double factorial definition 5.3: Scalar 5.3 Scalar definition 5.4: Vector 5.4 Vector definition 5.5: Linear combination 5.5 Linear combinati… definition 5.7: Vector subspace 5.7 Vector subspace definition 5.12: Subspace generated by a set of vectors 5.12 Subspace generat… definition 5.14: Linear independence 5.14 Linear independe… definition 5.15: Basis 5.15 Basis definition 5.16: Dimension 5.16 Dimension definition 5.17: Components of a vector 5.17 Components of a… definition 5.18: Inner product 5.18 Inner product definition 5.19: Norm 5.19 Norm definition 5.22: Metric associated with a norm 5.22 Metric associate… proposition 5.2: Jacobi's formula, column form 5.2 Jacobi's formula… proposition 5.20: Cauchy–Schwarz inequality 5.20 Cauchy–Schwarz i… proposition 5.28: Gram–Schmidt 5.28 Gram–Schmidt corollary 5.29: Orthogonal decomposition 5.29 Orthogonal decom… proposition 5.31: Gram criterion 5.31 Gram criterion lemma 5.33: Determinant through the Levi–Civita symbol 5.33 Determinant thro… lemma 5.34: Contraction of two Levi–Civita symbols 5.34 Contraction of t… proposition 5.35: The identities of the vector algebra of ℝ^3 5.35 The identities o… lemma 5.38: Exchange and completion 5.38 Exchange and com… theorem 5.40: Rank–nullity 5.40 Rank–nullity proposition 5.42: The adjoint exists, is unique, and is linear 5.42 The adjoint exis… theorem 5.43: The four fundamental subspaces 5.43 The four fundame… proposition 5.45: prop:lin-matrix-unique 5.45 proposition equation 5.3: eq:lin-binomial eq. (5.3) equation 5.10: eq:lin-trig-power-cos eq. (5.10) equation 5.18: eq:lin-angle-def eq. (5.18) equation 5.19: eq:lin-leibniz-det eq. (5.19) equation 5.29: eq:lin-indepli2 eq. (5.29) equation 5.44: eq:lin-norm-assoc eq. (5.44) equation 5.49: eq:lin-orthonormality eq. (5.49) equation 5.52: eq:lin-orthogonal-complement eq. (5.52) equation 5.74: eq:lin-matrix-rep eq. (5.74) equation 5.81: eq:lin-GL-matrices eq. (5.81) equation 5.86: eq:lin-functional3 eq. (5.86) equation 5.87: eq:lin-dual-expansion eq. (5.87) equation 5.102: eq:lin-eigenspace eq. (5.102) The chain of Linear Algebra and Representation Theory: 39 of 174 objects, read left to right from what the chapter assumes to what tests it. Solid lines are declared logical edges, dashed ones were inferred from the structure of the source. Click any node to open its own chain.