Ch. 1 Matrix Algebra 1 Some Terminology A matrix is a rectangular array of numbers, denoted 1 ai1 ai2 aik where a subscribed element of a matrix is always read as arou, column. Here we confine the element to be real number a vector is a matrix with one row or one column. Therefore a row vector is Alxk and a column vector is AixI and commonly denoted as ak and ai,respec- tively. In the followings of this course, we follow conventional custom to say that a vector is a columnvector except for particular mention The dimension of a matrix is the numbers of rows and columns it contained If i equals to k, then A is a square matrix. Several particular types of square matrices occur in econometrics (1).A symmetric matrix, a is one in which aik=ak: for all i and k. (e2).A diagonal matrix is a square matrix whose nonzero elements appears on the main diagonal, moving from upper left to lower right (3). A scalar matrix is a diagonal matrix with the same values in all diagonal elements (4). An identity matrix is a scalar matrix with ones on the diagonal. This matrix is always denoted as I. A subscript is sometimes included to indicate its size. for example 010 001 (5). A triangular matrix is one that has only zeros either above or below the main diagonalCh. 1 Matrix Algebra 1 Some Terminology A matrix is a rectangular array of numbers, denoted Ai×k = [aik] =         a11 a12 . . . a1k a21 a22 . . . a2k . . . . . . . . . . . . . . . . . . ai1 ai2 . . . aik         , where a subscribed element of a matrix is always read as arow,column. Here we confine the element to be real number. A vector is a matrix with one row or one column. Therefore a row vector is A1×k and a column vector is Ai×1 and commonly denoted as a ′ k and ai , respec￾tively. In the followings of this course, we follow conventional custom to say that a vector is a columnvector except for particular mention. The dimension of a matrix is the numbers of rows and columns it contained. If i equals to k, then A is a square matrix. Several particular types of square matrices occur in econometrics. (1). A symmetric matrix, A is one in which aik = aki for all i and k. (2). A diagonal matrix is a square matrix whose nonzero elements appears on the main diagonal, moving from upper left to lower right. (3). A scalar matrix is a diagonal matrix with the same values in all diagonal elements (4). An identity matrix is a scalar matrix with ones on the diagonal. This matrix is always denoted as I. A subscript is sometimes included to indicate its size. for example, I3 =   1 0 0 0 1 0 0 0 1  . (5). A triangular matrix is one that has only zeros either above or below the main diagonal. 1