sets and maps appropriate syntax to make use of - array multi-dimensional arrays are not handled at the hardware level insteadthe programming language typically provides its own mechanism for creating and managing multi-dimensional arrays as we saw earliera one-dimensional array is composed of group of sequential elements stored in successive memory locations the index used to reference particular element is simply the offset from the first element in the array in most programming languagesa multi-dimensional array is actually created and stored in memory as one-dimensional array with this organizationa multi-dimensional array is simply an abstract view of physical one-dimensional data structure array storage one-dimensional array is commonly used to physically store arrays of higher dimensions consider two-dimensional array divided into table of rows and columns as illustrated in figure how can the individual elements of the table be stored in the one-dimensional structure while maintaining direct access to the individual table elementsthere are two common approaches the elements can be stored in row-major order or column-major order most high-level programming languages use row-major orderwith fortran being one of the few languages that uses column-major ordering to store and manage - arrays figure the abstract view of sample two-dimensional array in row-major orderthe individual rows are stored sequentiallyone at timeas illustrated in figure the first row of elements are stored in the first sequential elements of the - arraythe second row of elements are stored in the next five sequential elementsand so forth in column-major orderthe - array is stored sequentiallyone entire column at timeas illustrated in figure the first column of elements are stored in the first sequential elements of the - arrayfollowed by the elements of the second columnand so on for larger dimensionsa similar approach can be used with three-dimensional arraythe individual tables can be stored contiguously using either row-major or column-major ordering as the number of dimensions growall elements within single instance of each dimension are stored contiguously before the next instance for examplegiven four-dimensional arraywhich can be thought of as an array of boxesall elements of an individual box ( - arrayare stored before the next box