Index

• ${\mathrm{[}\overrightarrow{v}\mathrm{]}}_{\mathrm{B}}$ Definition 2.42
• $\mathrm{⟨}\mathrm{\cdot }\mathrm{,}\mathrm{\cdot }\mathrm{⟩}$ Definition 3.4
• $\exists$ 1
• $||\overrightarrow{x}||$ (norm) 3.A
• $\mathrm{\oplus }$ Definition 6.37
• associative F5.
• basis Definition 2.24
• bijective Definition 4.38
• bilinear form Definition 3.4
• binary operation F1.
• $c_A(\lambda )$ 4.B
• ${}_{\mathrm{C}}\mathrm{[}T\mathrm{]}_{\mathrm{B}}$ Definition 4.4
• change of basis matrix Definition 4.48
• characteristic polynomial 4.B, 6.A
• codomain Definition 4.1
• column operation 1.B
• column space Definition 2.46
• column vector 3.A
• commutative F3.
• complex numbers 1
• coordinate matrix Definition 2.42
• coordinates 2.A, Definition 2.42
• degree of a polynomial Exercise 2.10
• $\mathrm{diag}(a_{11},\mathrm{\cdots },a_{nn})$ iii.
• diagonal 1.C
• diagonalizable 4.H, Definition 4.53
• dimension Definition 2.32
• Dimension theorem Theorem 4.24
• direct sum Definition 6.37
• distance 3.A
• domain Definition 4.1
• $\overrightarrow{e_i}$ ii.
• e.c.o. 1.B
• e.r.o. Definition 1.3
• eigenspace Exercise 4.12
• eigenvalue Definition 4.10
• eigenvector Definition 4.10
• elementary column operation 1.B
• elementary row operation Definition 1.3
• equivalence relation Exercise 1.19, Exercise 4.65
• field 1.A
• field axioms 1.A
• field of scalars 2.A
• finite-dimensional 2.D
• formal power series Exercise 2.70
• Fourier series Exercise 3.49
• Gram-Schmidt process 3.E
• idempotent ii.
• identity transformation Definition 4.48
• image Definition 4.15
• injective Definition 4.31
• inner product 3.B
• inner product space 3.C
• inverse matrix 1.C
• invertible 1.C
• isomorphic Definition 4.45
• JNF Definition 6.39
• Jordan block Definition 6.35
• Jordan chain Definition 6.28
• Jordan normal form Definition 6.39
• leading principal minor 5.B
• linear combination Definition 2.3
• linear transformation Definition 4.1
• lower triangular 1.C
• MATH105 1.B, 1.B, 2.D, 4.A, 4.B, 4.C, 4.E
• MATH112 4.F
• MATH115 3.C
• MATH210 Example 3.15, Exercise 3.49
• MATH215 Exercise 1.28
• MATH225 4.F
• MATH230 iii., Chapter 3, 4.A, 5.C
• MATH235 4.D
• MATH314 Chapter 3
• MATH317 2.D, Exercise 2.69, ii., Chapter 3, 3.C, Chapter 5
• MATH318 Chapter 6
• MATH319 Chapter 6
• MATH321 Exercise 6.72
• MATH327 Chapter 3, Chapter 5
• MATH329 Chapter 3
• MATH330 Chapter 5
• MATH332 Chapter 5
• MATH411 Chapter 5
• MATH451 Chapter 5
• MATH452 4.D
• matrix of a linear transformation Definition 4.4
• matrix square root 5.C, Definition 5.19
• monic 6.B
• nilpotent iii.
• null space 4.C
• nullity 4.D
• one-to-one 4.F
• orthogonal 3.D
• orthogonal matrix 5.A
• orthonormal Definition 3.21
• ${𝒫}_n(F)$ v.
• polynomials v., Exercise 2.65
• positive definite
  • form 3.B
  • matrix 5.B
• positive semi-definite matrix 5.C
• rank 4.D
• rational function Exercise 1.28
• real numbers 1
• reduced row echelon form Definition 1.9
• row operation Definition 1.3
• row space Definition 2.46
• row-equivalent 1.B
• self-adjoint Exercise 4.71
• similar matrices Definition 4.53
• skew-symmetric iii.
• solution space ii.
• span of vectors Definition 2.13
• spectral decomposition Theorem 5.7
• standard basis ii.
• submatrix 5.B
• subspace Definition 2.7
  • spanned by 2.B
• surjective Definition 4.35
• symmetric bilinear form 3.B
• symmetric matrix ii., Theorem 3.11
• system of linear equations 4.E
• ${\mathrm{\cdot }}^T$ 3.A
• trace Exercise 3.48, iii.
• transpose 3.A
• unit vector 3.A
• upper triangular 1.C
• vector 2.A, 2.A
• vector space 2.A
  • axioms 2.A