## Index Index

1-1, Definition

\(\mathcal{B}\)-coordinates, Definition

affine map, Investigation

augmented matrix, Investigation

basis, Paragraph Section Definition

standard basis, Paragraph

coefficient matrix, Investigation

column space, Paragraph

conjugate, Paragraph Definition

consistent, Example

coordinate system, Definition

cross product, Paragraph

determinant, Section Investigation

diagonal matrix, Definition

diagonalizable, Definition

dimension, Definition

dot product, Paragraph

eigenvalue, Definition

eigenvector, Definition

elementary vectors, Paragraph Subsection

elimination and back substitution, Investigation

free variable, Example

function, Definition

Gram-Schmidt Orthogonalization, Investigation

homogeneous, Example

homomorphism, Section Definition

kernel, Definition

left inverse, Definition

linear combination, Paragraph

linear independence, Section

linear map, Definition

linear system, Section

linearly dependent, Definition

linearly independent, Definition

one-to-one, Definition

onto, Definition

orthogonal basis, Definition

orthonormal basis, Definition

overdetermined, Example

scalar, Paragraph

similar, Paragraph

similar matrices, Definition

similar matrix, Definition

standard basis, Paragraph

system of equations, Investigation

vector, Definition

elementary vectors, Paragraph

unit vector, Paragraph

vector equation, Paragraph

vector equation, Paragraph

vector space, Section Definition

subspace, Paragraph

vectors, Section

zero divisor, Exercise