×
Log in to StudySoup
Get Full Access to Math - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Math - Textbook Survival Guide
Textbooks / Math / Elementary Linear Algebra 7

Elementary Linear Algebra 7th Edition - Solutions by Chapter

Elementary Linear Algebra | 7th Edition | ISBN: 9781133110873 | Authors: Ron Larson

Full solutions for Elementary Linear Algebra | 7th Edition

ISBN: 9781133110873

Elementary Linear Algebra | 7th Edition | ISBN: 9781133110873 | Authors: Ron Larson

Elementary Linear Algebra | 7th Edition - Solutions by Chapter

Elementary Linear Algebra was written by and is associated to the ISBN: 9781133110873. The full step-by-step solution to problem in Elementary Linear Algebra were answered by , our top Math solution expert on 01/03/18, 08:36PM. Since problems from 7 chapters in Elementary Linear Algebra have been answered, more than 9773 students have viewed full step-by-step answer. This textbook survival guide was created for the textbook: Elementary Linear Algebra, edition: 7. This expansive textbook survival guide covers the following chapters: 7.

Key Math Terms and definitions covered in this textbook
  • Cayley-Hamilton Theorem.

    peA) = det(A - AI) has peA) = zero matrix.

  • Change of basis matrix M.

    The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

  • Complex conjugate

    z = a - ib for any complex number z = a + ib. Then zz = Iz12.

  • Diagonalization

    A = S-1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k S-I.

  • Dimension of vector space

    dim(V) = number of vectors in any basis for V.

  • Distributive Law

    A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

  • Eigenvalue A and eigenvector x.

    Ax = AX with x#-O so det(A - AI) = o.

  • Free variable Xi.

    Column i has no pivot in elimination. We can give the n - r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

  • Gauss-Jordan method.

    Invert A by row operations on [A I] to reach [I A-I].

  • Hessenberg matrix H.

    Triangular matrix with one extra nonzero adjacent diagonal.

  • Indefinite matrix.

    A symmetric matrix with eigenvalues of both signs (+ and - ).

  • Jordan form 1 = M- 1 AM.

    If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

  • Kronecker product (tensor product) A ® B.

    Blocks aij B, eigenvalues Ap(A)Aq(B).

  • Nullspace N (A)

    = All solutions to Ax = O. Dimension n - r = (# columns) - rank.

  • Orthonormal vectors q 1 , ... , q n·

    Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q -1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

  • Projection p = a(aTblaTa) onto the line through a.

    P = aaT laTa has rank l.

  • Random matrix rand(n) or randn(n).

    MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

  • Row space C (AT) = all combinations of rows of A.

    Column vectors by convention.

  • Saddle point of I(x}, ... ,xn ).

    A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

  • Transpose matrix AT.

    Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and A-I are BT AT and (AT)-I.

×
Log in to StudySoup
Get Full Access to Math - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Math - Textbook Survival Guide
×
Reset your password