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Textbooks > Math > Mathematics for the International Student: Mathematics SL 3

Mathematics for the International Student: Mathematics SL 3rd Edition - Solutions by Chapter

Full solutions for Mathematics for the International Student: Mathematics SL | 3rd Edition

ISBN: 9781921972089

Mathematics for the International Student: Mathematics SL | 3rd Edition - Solutions by Chapter

Since problems from 25 chapters in Mathematics for the International Student: Mathematics SL have been answered, more than 5525 students have viewed full step-by-step answer. This textbook survival guide was created for the textbook: Mathematics for the International Student: Mathematics SL, edition: 3. Mathematics for the International Student: Mathematics SL was written by and is associated to the ISBN: 9781921972089. The full step-by-step solution to problem in Mathematics for the International Student: Mathematics SL were answered by , our top Math solution expert on 03/15/18, 06:04PM. This expansive textbook survival guide covers the following chapters: 25.

Key Math Terms and definitions covered in this textbook
  • Associative Law (AB)C = A(BC).

    Parentheses can be removed to leave ABC.

  • Back substitution.

    Upper triangular systems are solved in reverse order Xn to Xl.

  • Block matrix.

    A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

  • Cholesky factorization

    A = CTC = (L.J]))(L.J]))T for positive definite A.

  • Circulant matrix C.

    Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn - l . Cx = convolution c * x. Eigenvectors in F.

  • Conjugate Gradient Method.

    A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax - x Tb over growing Krylov subspaces.

  • Elimination matrix = Elementary matrix Eij.

    The identity matrix with an extra -eij in the i, j entry (i #- j). Then Eij A subtracts eij times row j of A from row i.

  • Graph G.

    Set of n nodes connected pairwise by m edges. A complete graph has all n(n - 1)/2 edges between nodes. A tree has only n - 1 edges and no closed loops.

  • Hankel matrix H.

    Constant along each antidiagonal; hij depends on i + j.

  • Incidence matrix of a directed graph.

    The m by n edge-node incidence matrix has a row for each edge (node i to node j), with entries -1 and 1 in columns i and j .

  • Inverse matrix A-I.

    Square matrix with A-I A = I and AA-l = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B-1 A-I and (A-I)T. Cofactor formula (A-l)ij = Cji! detA.

  • Length II x II.

    Square root of x T x (Pythagoras in n dimensions).

  • Multiplication Ax

    = Xl (column 1) + ... + xn(column n) = combination of columns.

  • Nullspace matrix N.

    The columns of N are the n - r special solutions to As = O.

  • Pivot.

    The diagonal entry (first nonzero) at the time when a row is used in elimination.

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

    Column vectors by convention.

  • Similar matrices A and B.

    Every B = M-I AM has the same eigenvalues as A.

  • Standard basis for Rn.

    Columns of n by n identity matrix (written i ,j ,k in R3).

  • Trace of A

    = sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

  • Volume of box.

    The rows (or the columns) of A generate a box with volume I det(A) I.

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