# Index of Definitions for Chapter 1

Additive inverse 12

Basis 43

Cancellation law 12

Column vector 8

Chain 60

Degree of a polynomial 10

Diagonal entries of a matrix 8

Diagonal matrix 19

Dimension 47

Finite-dimensional space 47

Generates 31

Infinite-dimensional space 47

Lagrange interpolation formula 53

Lagrange polynomials 52

Linear combination 25

Linearly dependent 37

Linearly independent 38

Matrix 8

Maximal element of a family of sets 59

Maximal linearly independent subset 60

`n`-tuple 8

Polynomial 10

Row vector 8

Scalar 7

Scalar multiplication 6

Sequence 11

Span of a subset 30

Spans 31

Square matrix 9

Standard basis for ${\text{F}}^{n}$ 43

Standard basis for ${\text{P}}_{n}(F)$ 44

Subspace 17

Subspace generated by the elements of a set 31

Symmetric matrix 18

Trace 19

Transpose 18

Upper triangular matrix 19

Trivial representation of 0 37

Vector 7

Vector addition 6

Vector space 6

Zero matrix 9

Zero polynomial 10

Zero subspace 17

Zero vector 12

Zero vector space 15