Cambridge,Įngland: Cambridge University Press, 1955. Matrices and Some Applications to Dynamics and Differential Equations. Dodgson,Įlementary Treatise on Determinants, with Their Application to Simultaneous LinearĮquations and Algebraical Geometry. Orlando, FL: Academic Press, pp. 176-191,Īlgebra and Linear Models, 2nd ed. "Matrices." §4.2 in Mathematical Methods for Physicists, 3rd ed. Topic in the MathWorld classroom Explore with Wolfram|Alpha Matrix, Ill-Conditioned Matrix, Incidence Matrix, IrreducibleĬommon Multiple Matrix, LU Decomposition, Matrix, Bourque-Ligh Conjecture, Cartan Matrix, Circulantĭecomposition Theorem, Eigenvector, Elementary See also Adjacency Matrix, Adjoint, Alternating Sign Matrix, Antisymmetric Introduces the unfortunate notational ambiguity between matrices of the form and the binomial coefficient In this work, matrices are represented using square brackets as delimiters, but in the general literature, they are more commonlyĭelimited using parentheses. Matrices include the identity matrix, with (where is the
Inch by 11 inch paper is 8 1/2 inches wide and 11 inches high).Ī matrix is said to be square if, and rectangular Windows, (in which the width is listed first followed by the height e.g., 8 1/2 One used for expressing measurements of a painting on canvas (where height comesįirst then width), it is opposite that used to measure paper, room dimensions, and Note that while this convention matches the (i.e., lower right) term, so the indices of the lastĮlement in the above matrix identify it as an matrix. Remember which index refers to which direction, identify the indices of the last With real coefficients is sometimes denoted. The transformation given by the system of equationsĪn matrix consists of rows and columns, and the set of matrices In his 1867 treatise on determinants, C. L. Dodgson (Lewis Carroll) objected to the use of the term "matrix," stating, "I am aware that the word 'Matrix' is already in use to express the very meaning for which I use the word 'Block' but surely the former word means rather the mould, or form, into which algebraical quantities may be introduced, than an actual assemblage of such quantities." However, Dodgson's objections have passed unheeded and the term "matrix" has stuck. To use the terminology in its modern form in papers of 18 (Katz 1993). Identically zero." However, it remained up to Sylvester's collaborator Cayley That can be formed by rejecting any one column at pleasure out of this matrix are "Form the rectangular matrix consisting of rows and columns. Sylvester (1851) subsequently used the term matrix informally, stating In its conventional usage to mean "the place from which something else originates" The array itself (Kline 1990, p. 804), Sylvester used the term "matrix" Interested in the determinant formed from the rectangular array of number and not
Which we may form various systems of determinants by fixing upon a number, and selectingĬorresponding of th order." Because Sylvester was This will not in itself representĪ determinant, but is, as it were, a Matrix out of In his 1851 paper, Sylvester wrote, "For this purpose we must commence, not with a square, but with an oblong arrangement of terms consisting, suppose, of lines and columns. The matrix, and its close relative the determinant,Īre extremely important concepts in linear algebra,Īnd were first formulated by Sylvester (1851) and Cayley. In particular, everyīy a matrix, and every matrix corresponds to a unique linear A matrix is a concise and useful way of uniquely representing and working with linear transformations.