Math1410text.idx

\indexentry{set ! definition of|hyperpage}{1}
\indexentry{set ! verbal description|hyperpage}{1}
\indexentry{set ! roster method|hyperpage}{1}
\indexentry{set ! set-builder notation|hyperpage}{1}
\indexentry{set-builder notation|hyperpage}{1}
\indexentry{set ! inclusion|hyperpage}{2}
\indexentry{$\in $|hyperpage}{2}
\indexentry{set ! exclusion|hyperpage}{2}
\indexentry{$\notin  $|hyperpage}{2}
\indexentry{subset ! definition of|hyperpage}{2}
\indexentry{set ! intersection|hyperpage}{2}
\indexentry{intersection of two sets|hyperpage}{2}
\indexentry{set ! union|hyperpage}{2}
\indexentry{union of two sets|hyperpage}{2}
\indexentry{set ! empty|hyperpage}{3}
\indexentry{empty set|hyperpage}{3}
\indexentry{diagram ! Venn Diagram|hyperpage}{3}
\indexentry{Venn Diagram|hyperpage}{3}
\indexentry{relatively prime|hyperpage}{7}
\indexentry{Cartesian coordinate plane|hyperpage}{12}
\indexentry{$x$-axis|hyperpage}{12}
\indexentry{$y$-axis|hyperpage}{12}
\indexentry{ordered pair|hyperpage}{12}
\indexentry{abscissa|hyperpage}{12}
\indexentry{$x$-coordinate|hyperpage}{12}
\indexentry{ordinate|hyperpage}{12}
\indexentry{$y$-coordinate|hyperpage}{12}
\indexentry{coordinates ! Cartesian|hyperpage}{12}
\indexentry{Cartesian coordinates|hyperpage}{12}
\indexentry{origin|hyperpage}{12}
\indexentry{absolute value|hyperpage}{14}
\indexentry{quadrants|hyperpage}{14}
\indexentry{distance ! definition|hyperpage}{14}
\indexentry{distance ! distance formula|hyperpage}{14}
\indexentry{midpoint ! definition of|hyperpage}{15}
\indexentry{midpoint ! midpoint formula|hyperpage}{15}
\indexentry{numbers ! complex|hyperpage}{19}
\indexentry{complex numbers|hyperpage}{19}
\indexentry{imaginary unit, $i$|hyperpage}{19}
\indexentry{complex number ! imaginary unit, $i$|hyperpage}{19}
\indexentry{complex number ! definition of|hyperpage}{19}
\indexentry{complex numbers ! equality|hyperpage}{20}
\indexentry{complex numbers ! addition|hyperpage}{20}
\indexentry{complex numbers ! multiplication|hyperpage}{20}
\indexentry{complex number ! complex conjugate ! definition of|hyperpage}{21}
\indexentry{conjugate ! complex conjugate ! definition of|hyperpage}{21}
\indexentry{complex number ! conjugate ! properties of|hyperpage}{22}
\indexentry{conjugate of a complex number ! properties of|hyperpage}{22}
\indexentry{Fundamental Theorem of Algebra|hyperpage}{26}
\indexentry{Fundamental Theorem of Algebra|hyperpage}{26}
\indexentry{theorem ! Fundamental Theorem of Algebra|hyperpage}{26}
\indexentry{Complex Factorization Theorem|hyperpage}{26}
\indexentry{factorization ! over the complex numbers|hyperpage}{26}
\indexentry{rectangular coordinates ! also known as Cartesian coordinates|hyperpage}{28}
\indexentry{coordinates ! rectangular|hyperpage}{28}
\indexentry{polar coordinates ! definition of|hyperpage}{28}
\indexentry{coordinates ! polar|hyperpage}{28}
\indexentry{polar coordinates ! pole|hyperpage}{28}
\indexentry{polar coordinates ! polar axis|hyperpage}{28}
\indexentry{polar coordinates ! conversion into rectangular|hyperpage}{31}
\indexentry{rectangular coordinates ! conversion into polar|hyperpage}{31}
\indexentry{complex number ! definition of|hyperpage}{34}
\indexentry{complex number ! real part|hyperpage}{34}
\indexentry{real part of a complex number|hyperpage}{34}
\indexentry{imaginary part of a complex number|hyperpage}{34}
\indexentry{complex number ! imaginary part|hyperpage}{34}
\indexentry{real axis|hyperpage}{34}
\indexentry{imaginary axis|hyperpage}{34}
\indexentry{complex plane|hyperpage}{34}
\indexentry{complex number ! rectangular form|hyperpage}{34}
\indexentry{rectangular form of a complex number|hyperpage}{34}
\indexentry{complex number ! modulus ! definition of|hyperpage}{34}
\indexentry{modulus of a complex number ! definition of|hyperpage}{34}
\indexentry{complex number ! argument ! definition of|hyperpage}{34}
\indexentry{argument ! of a complex number ! definition of|hyperpage}{34}
\indexentry{complex number ! principal argument|hyperpage}{34}
\indexentry{principal argument of a complex number|hyperpage}{34}
\indexentry{complex number ! modulus ! properties of|hyperpage}{36}
\indexentry{modulus of a complex number ! properties of|hyperpage}{36}
\indexentry{product rule ! for the modulus of a complex number|hyperpage}{36}
\indexentry{power rule ! for the modulus of a complex number|hyperpage}{36}
\indexentry{quotient rule ! for the modulus of a complex number|hyperpage}{36}
\indexentry{complex number ! argument ! properties of|hyperpage}{37}
\indexentry{argument ! of a complex number ! properties of|hyperpage}{37}
\indexentry{cis($\theta$)|hyperpage}{38}
\indexentry{complex number ! polar form ! cis-notation|hyperpage}{38}
\indexentry{polar form of a complex number|hyperpage}{38}
\indexentry{product rule ! for complex numbers|hyperpage}{39}
\indexentry{DeMoivre's Theorem|hyperpage}{39}
\indexentry{power rule ! for complex numbers|hyperpage}{39}
\indexentry{quotient rule ! for complex numbers|hyperpage}{39}
\indexentry{$n^{\textrm  {th}}$ root ! of a complex number|hyperpage}{43}
\indexentry{complex number ! $n^{\textrm  {th}}$ root|hyperpage}{43}
\indexentry{$n^{\textrm  {th}}$ root ! of a complex number|hyperpage}{44}
\indexentry{complex number ! $n^{\textrm  {th}}$ root|hyperpage}{44}
\indexentry{$n^{\textrm  {th}}$ Roots of Unity|hyperpage}{48}
\indexentry{complex number ! $n^{\textrm  {th}}$ Roots of Unity|hyperpage}{48}
\indexentry{Roots of Unity|hyperpage}{48}
\indexentry{right hand rule!of Cartesian coordinates|hyperpage}{51}
\indexentry{distance!between points in space|hyperpage}{52}
\indexentry{planes!coordinate plane|hyperpage}{52}
\indexentry{planes!introduction|hyperpage}{52}
\indexentry{vectors|hyperpage}{55}
\indexentry{vectors!definition|hyperpage}{55}
\indexentry{vectors!norm|hyperpage}{55}
\indexentry{vectors!magnitude|hyperpage}{55}
\indexentry{norm|hyperpage}{55}
\indexentry{magnitude of vector|hyperpage}{55}
\indexentry{terminal point|hyperpage}{55}
\indexentry{initial point|hyperpage}{55}
\indexentry{r@$\mathbb{R}$|hyperpage}{55}
\indexentry{vectors!component form|hyperpage}{56}
\indexentry{vectors!algebra of|hyperpage}{57}
\indexentry{vectors!resultant|hyperpage}{57}
\indexentry{Parallelogram Law|hyperpage}{57}
\indexentry{vectors!Parallelogram Law|hyperpage}{57}
\indexentry{Head To Tail Rule|hyperpage}{57}
\indexentry{vectors!Head To Tail Rule|hyperpage}{57}
\indexentry{vectors!zero vector|hyperpage}{57}
\indexentry{parallel vectors|hyperpage}{59}
\indexentry{vectors!parallel|hyperpage}{59}
\indexentry{vectors!algebraic properties|hyperpage}{59}
\indexentry{vectors!unit vector|hyperpage}{60}
\indexentry{unit vector|hyperpage}{60}
\indexentry{vectors!parallel|hyperpage}{61}
\indexentry{parallel vectors|hyperpage}{61}
\indexentry{unit vector!properties|hyperpage}{61}
\indexentry{vectors!unit vector|hyperpage}{61}
\indexentry{vectors!standard unit vector|hyperpage}{62}
\indexentry{unit vector!standard unit vector|hyperpage}{62}
\indexentry{dot product!definition|hyperpage}{67}
\indexentry{vectors!dot product|hyperpage}{67}
\indexentry{dot product!properties|hyperpage}{68}
\indexentry{vectors!dot product|hyperpage}{68}
\indexentry{dot product!properties|hyperpage}{68}
\indexentry{vectors!dot product|hyperpage}{68}
\indexentry{orthogonal|hyperpage}{70}
\indexentry{perpendicular|hyperindexformat{\see{orthogonal}}}{70}
\indexentry{vectors!orthogonal|hyperpage}{70}
\indexentry{orthogonal projection|hyperpage}{72}
\indexentry{vectors!orthogonal projection|hyperpage}{72}
\indexentry{orthogonal decomposition of vectors|hyperpage}{73}
\indexentry{orthogonal!decomposition|hyperpage}{73}
\indexentry{vectors!orthogonal decomposition|hyperpage}{73}
\indexentry{work|hyperpage}{75}
\indexentry{vectors!cross product|hyperpage}{77}
\indexentry{cross product!definition|hyperpage}{77}
\indexentry{vectors!cross product|hyperpage}{80}
\indexentry{cross product!properties|hyperpage}{80}
\indexentry{vectors!cross product|hyperpage}{81}
\indexentry{cross product!properties|hyperpage}{81}
\indexentry{cross product!applications|hyperpage}{82}
\indexentry{cross product!applications!area of parallelogram|hyperpage}{82}
\indexentry{cross product!applications!volume of parallelepiped|hyperpage}{84}
\indexentry{cross product!applications!torque|hyperpage}{85}
\indexentry{lines|hyperpage}{89}
\indexentry{lines!equations for|hyperpage}{90}
\indexentry{lines!skew|hyperpage}{91}
\indexentry{lines!parallel|hyperpage}{91}
\indexentry{lines!intersecting|hyperpage}{91}
\indexentry{vectors!normal vector|hyperpage}{101}
\indexentry{normal vector|hyperpage}{101}
\indexentry{planes!normal vector|hyperpage}{101}
\indexentry{planes!equations of|hyperpage}{101}
\indexentry{matrix!definition|hyperpage}{112}
\indexentry{row vector|hyperpage}{112}
\indexentry{column vector|hyperpage}{112}
\indexentry{vector ! row|hyperpage}{112}
\indexentry{vector ! column|hyperpage}{112}
\indexentry{matrix!equality|hyperpage}{113}
\indexentry{matrix!addition|hyperpage}{114}
\indexentry{scalar|hyperpage}{115}
\indexentry{matrix!scalar multiplication|hyperpage}{115}
\indexentry{linear combination|hyperpage}{115}
\indexentry{zero matrix|hyperpage}{117}
\indexentry{matrix!the zero matrix|hyperpage}{117}
\indexentry{matrix!arithmetic properties|hyperpage}{118}
\indexentry{vector space|hyperpage}{121}
\indexentry{vector space ! of column vectors|hyperpage}{121}
\indexentry{linear combination|hyperpage}{122}
\indexentry{span|hyperpage}{124}
\indexentry{linearly dependent|hyperpage}{126}
\indexentry{dependent ! linear|hyperpage}{126}
\indexentry{linearly independent|hyperpage}{126}
\indexentry{independent ! linear|hyperpage}{126}
\indexentry{subspace|hyperpage}{128}
\indexentry{subspace ! span|hyperpage}{134}
\indexentry{subspace ! trivial|hyperpage}{134}
\indexentry{dimension|hyperpage}{135}
\indexentry{basis|hyperpage}{135}
\indexentry{matrix!multiplication|hyperpage}{141}
\indexentry{identity matrix|hyperpage}{147}
\indexentry{matrix!identity matrix|hyperpage}{147}
\indexentry{matrix!multiplication!properties|hyperpage}{148}
\indexentry{matrix transformation|hyperpage}{152}
\indexentry{transformation ! matrix|hyperpage}{152}
\indexentry{linear transformation!definition|hyperpage}{169}
\indexentry{linear transformation!standard matrix of|hyperpage}{173}
\indexentry{linear transformation!and \ensuremath  {\mathaccentV {vec}17E{\text  {\it  0}}}|hyperpage}{174}
\indexentry{standard unit vector|hyperpage}{174}
\indexentry{linear transformation!standard matrix of|hyperpage}{175}
\indexentry{linear transformation!conditions on|hyperpage}{178}
\indexentry{range ! of a linear transformation|hyperpage}{181}
\indexentry{column space|hyperpage}{182}
\indexentry{null space|hyperpage}{183}
\indexentry{rank ! in terms of column space|hyperpage}{184}
\indexentry{linear equation|hyperpage}{189}
\indexentry{system of linear equations!definition|hyperpage}{189}
\indexentry{system of linear equations!solution|hyperpage}{189}
\indexentry{solution|hyperpage}{189}
\indexentry{matrix ! of coefficients|hyperpage}{193}
\indexentry{augmented matrix|hyperpage}{193}
\indexentry{matrix!augmented|hyperpage}{193}
\indexentry{elementary row operations|hyperpage}{198}
\indexentry{reduced echelon form|hyperpage}{199}
\indexentry{reduced row echelon form|hyperpage}{199}
\indexentry{row echelon form|hyperpage}{199}
\indexentry{leading one|hyperpage}{199}
\indexentry{Gaussian elimination|hyperpage}{200}
\indexentry{back substitution|hyperpage}{201}
\indexentry{Gaussian elimination!forward steps|hyperpage}{202}
\indexentry{Gaussian elimination!backward steps|hyperpage}{202}
\indexentry{Gaussian elimination|hyperpage}{203}
\indexentry{solution!types|hyperpage}{210}
\indexentry{solution!unique|hyperpage}{210}
\indexentry{solution!infinite|hyperpage}{210}
\indexentry{solution!none|hyperpage}{210}
\indexentry{system of linear equations!consistent|hyperpage}{210}
\indexentry{system of linear equations!inconsistent|hyperpage}{210}
\indexentry{consistent|hyperpage}{210}
\indexentry{inconsistent|hyperpage}{210}
\indexentry{free variable|hyperpage}{211}
\indexentry{variable!free|hyperpage}{211}
\indexentry{parameter|hyperpage}{211}
\indexentry{variable!leading|hyperpage}{211}
\indexentry{solution!particular|hyperpage}{212}
\indexentry{solution!general|hyperpage}{212}
\indexentry{variable!dependent|hyperpage}{212}
\indexentry{variable!basic|hyperpage}{212}
\indexentry{basic variable|hyperpage}{212}
\indexentry{variable!independent|hyperpage}{212}
\indexentry{variable!free|hyperpage}{212}
\indexentry{free variable|hyperpage}{212}
\indexentry{system of linear equations!consistent|hyperpage}{213}
\indexentry{leading one|hyperpage}{213}
\indexentry{solution!infinitely many|hyperpage}{213}
\indexentry{system of linear equations!consistent|hyperpage}{213}
\indexentry{leading one|hyperpage}{213}
\indexentry{solution!infinitely many|hyperpage}{213}
\indexentry{system of linear equations!inconsistent|hyperpage}{214}
\indexentry{leading one|hyperpage}{214}
\indexentry{particular solution|hyperpage}{215}
\indexentry{solution!particular|hyperpage}{215}
\indexentry{problem solving|hyperpage}{222}
\indexentry{system of linear equations!homogeneous|hyperpage}{239}
\indexentry{homogeneous|hyperpage}{239}
\indexentry{solution!basic|hyperpage}{240}
\indexentry{basic solution|hyperpage}{240}
\indexentry{basis ! of a null space|hyperpage}{240}
\indexentry{consistent|hyperpage}{243}
\indexentry{system of linear equations!consistent|hyperpage}{243}
\indexentry{homogeneous|hyperpage}{243}
\indexentry{homogeneous|hyperpage}{244}
\indexentry{consistent|hyperpage}{244}
\indexentry{system of linear equations!consistent|hyperpage}{244}
\indexentry{solution!unique|hyperpage}{244}
\indexentry{solution!infinitely many|hyperpage}{244}
\indexentry{rank ! in terms of leading 1s|hyperpage}{245}
\indexentry{column ! pivot|hyperpage}{246}
\indexentry{pivot column|hyperpage}{246}
\indexentry{matrix!inverse|hyperpage}{263}
\indexentry{inverse!definition|hyperpage}{263}
\indexentry{inverse!uniqueness|hyperpage}{265}
\indexentry{inverse!computing|hyperpage}{267}
\indexentry{matrix!inverse|hyperpage}{267}
\indexentry{solution!unique|hyperpage}{269}
\indexentry{Invertible Matrix Theorem|hyperpage}{273}
\indexentry{inverse!properties|hyperpage}{273}
\indexentry{inverse!Invertible Matrix Theorem|hyperpage}{273}
\indexentry{diagonal|hyperpage}{278}
\indexentry{inverse!properties|hyperpage}{278}
\indexentry{matrix ! elementary|hyperpage}{281}
\indexentry{elementary matrix|hyperpage}{281}
\indexentry{transpose|hyperpage}{287}
\indexentry{transpose!definition|hyperpage}{287}
\indexentry{transpose!definition|hyperpage}{287}
\indexentry{matrix!transpose|hyperpage}{287}
\indexentry{diagonal!definition|hyperpage}{288}
\indexentry{triangular matrix!definition|hyperpage}{288}
\indexentry{matrix!diagonal|hyperpage}{288}
\indexentry{matrix!triangular|hyperpage}{288}
\indexentry{transpose!properties|hyperpage}{291}
\indexentry{symmetric|hyperpage}{293}
\indexentry{skew symmetric|hyperpage}{293}
\indexentry{transpose!symmetric|hyperpage}{293}
\indexentry{transpose!skew-symmetric|hyperpage}{293}
\indexentry{symmetric!definition|hyperpage}{293}
\indexentry{skew symmetric!definition|hyperpage}{293}
\indexentry{antisymmetric|hyperpage}{293}
\indexentry{symmetric!theorem|hyperpage}{293}
\indexentry{skew symmetric!theorem|hyperpage}{293}
\indexentry{pseudoinverse|hyperpage}{294}
\indexentry{trace!definition|hyperpage}{296}
\indexentry{trace!properties|hyperpage}{298}
\indexentry{determinant!of $2\times 2$ matrices|hyperpage}{300}
\indexentry{matrix!determinant|hyperpage}{300}
\indexentry{matrix!minor|hyperpage}{301}
\indexentry{matrix!cofactor|hyperpage}{301}
\indexentry{minor|hyperpage}{301}
\indexentry{cofactor|hyperpage}{301}
\indexentry{cofactor!expansion|hyperpage}{303}
\indexentry{matrix!determinant|hyperpage}{304}
\indexentry{determinant!definition|hyperpage}{304}
\indexentry{cofactor!expansion|hyperpage}{309}
\indexentry{determinant!of triangular matrices|hyperpage}{311}
\indexentry{triangular matrix!determinant|hyperpage}{311}
\indexentry{elementary row operations!and determinants|hyperpage}{312}
\indexentry{determinant!and elementary row operations|hyperpage}{312}
\indexentry{elementary matrix|hyperpage}{316}
\indexentry{matrix!elementary|hyperpage}{316}
\indexentry{determinant!properties|hyperpage}{316}
\indexentry{Invertible Matrix Theorem|hyperpage}{317}
\indexentry{Cramer's Rule|hyperpage}{320}
\indexentry{matrix!cofactor|hyperpage}{322}
\indexentry{cofactor!matrix|hyperpage}{322}
\indexentry{adjugate|hyperpage}{322}
\indexentry{matrix!adjugate|hyperpage}{322}
\indexentry{eigenvalue!definition|hyperpage}{328}
\indexentry{eigenvector!|hyperindexformat{\see{eigenvalue}}}{328}
\indexentry{characteristic polynomial|hyperpage}{331}
\indexentry{eigenvalue!finding|hyperpage}{331}
\indexentry{eigenvalue!properties|hyperpage}{348}
\indexentry{Invertible Matrix Theorem|hyperpage}{349}
\indexentry{similar matrices|hyperpage}{351}
\indexentry{matrix!similar|hyperpage}{351}
\indexentry{equivalence relation|hyperpage}{352}
\indexentry{similar matrices!properties of|hyperpage}{352}
\indexentry{multiplicity!of an eigenvalue|hyperpage}{353}
\indexentry{characteristic polynomial|hyperpage}{353}
\indexentry{multiplicity!algebraic|hyperpage}{353}
\indexentry{eigenspace|hyperpage}{354}
\indexentry{multiplicity!geometric|hyperpage}{355}
\indexentry{diagonalization|hyperpage}{356}
\indexentry{diagonalizable matrix|hyperpage}{357}
\indexentry{matrix!diagonalizable|hyperpage}{357}
\indexentry{multiplicity!and diagonalization|hyperpage}{360}
\indexentry{Jordan Canonical Form|hyperpage}{361}
\indexentry{diagonalization!orthogonal|hyperpage}{361}