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11.1: Creating Matrices and Arrays

  • Page ID
    85005
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    By Carey A. Smith

    For our purposes, an array is 2-dimensional set of numbers.

    A matrix is a 2-dimensional set of numbers that is used for linear algebra computations.

    MATLAB keeps track of the numbers of rows and columns of a matrix.

    User-defined matrices are typically defined in the following 2 equivalent ways:

    Method 1: Create a matrix in directly 2-dimensions

    M1 = [1 4 7 10
    2 5 8 11
    3 6 9 12]

    Method 2: Create a matrix on 1 line, with semicolons separating the rows:

    M2 = [1 4 7 10; 2 5 8 11; 3 6 9 12]

    This creates the same matrices, but is not as visually obvious. This method is often used in books to save space on a page.

    It is also possible to define MATLAB matrices (arrays) with 3 or more dimensions, but we will only use 2-dimensional arrays in this text.

    Built-in functions to create a matrix

    zeros(rows,cols)

    Example:
    z23 = zeros(2,3)

    Result:
    0 0 0
    0 0 0

    ones(rows,cols)
    Example:
    a32 = ones(3,2)
    1 1
    1 1
    1 1

    You can create a matrix of all constant values by multiplying a "ones" matrix by a constant.

    6*ones(rows,cols)
    a32_6 = 6*ones(3,2)
    6 6
    6 6
    6 6

    eye(n) = Identity matrix
    Example:
    I4 = eye(4)
    1 0 0 0
    0 1 0 0
    0 0 1 0
    0 0 0 1

    magic(n) = Magic square. The sums of all the rows, columns, and diagonals are the same in a magic square.

    Example:
    m3 = magic(3)
    8 1 6
    3 5 7
    4 9 2

    diag(v) When v is a vector, creates a square matrix with diagonal elements = v.

    v = [4, 9, 16]
    B = diag(v)
    4 0 0
    0 9 0
    0 0 16

    diag(M) When M is a matrix, this extracts the diagonal elements of matrix M.

    Example using magic square m3:

    diag(m3) = [8
    5
    2]

    pascal4 = pascal(4)
    1 1 1 1
    1 2 3 4
    1 3 6 10
    1 4 10 20
    It has binomial coefficients


    This page titled 11.1: Creating Matrices and Arrays is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Carey Smith.

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