Matrices Vocabulary Flash Cards

MATRIX

A matrix is a tabular representation of data. It is a rectangular arrangement of numbers in rows and columns, enclosed within brackets. Rows run horizontally and columns run vertically. A matrix is generally represented by an uppercase letter. The dimensions of a matrix are stated as "m by n" where 'm' is the number of rows and 'n' is the number of columns.

COLUMN MATRIX

A matrix with a single column

NULL MATRIX (ZERO MATRIX)

A matrix with only zeros as its elements is known as Null Matrix or Zero Matrix.

CRAMER'S RULE

A method for solving a linear system of equations using determinants.

SYMMETRIC MATRIX

A symmetric matrix is a square matrix that is equal to its transpose.

ADJACENCY MATRIX

Adjacency Matrix models a communication network. In such a matrix, a "1" in any row indicates that direct communication from vertex to another. A "0" indicates that direct communication is not possible.

INVERSE MATRIX

An Inverse Matrix is the inverse of a square matrix . It is also sometimes called a reciprocal matrix. For a matrix, A, the Inverse matrix is denoted by A─1 . The important relationship between a matrix and its inverse matrix is: A.A^─1 = I where is the identity matrix.

IDENTITY OPERATION

An equation or operation that holds for all values of the variables. In Matrix Algebra, when a matrix is multiplied by an identity matrix, we get back the original matrix. In real number addition and subtraction, identity is ZERO, in real number multiplication and division, identity is ONE. The determinant of an Identity Matrix is ONE. Identity Matrix is denoted by I

EQUAL MATRICES

Equal matrices are those matrices that have identical dimensions and identical elements at exactly the same locations.

IDENTITY MATRIX

Identity Matrix is a Square Matrix that has all ONES on in the Major Diagonal and ONLY ZEROs in all other locations.

DETERMINANT

In linear algebra, the determinant is an important value associated with a square matrix. For a 2x2 matrix, the Determinant is given by the difference between the product of the elements of the Major Diagonal and the product of the elements of Minor Diagonal. The general notation for determinant of a matrix A is IAI or det A.

ASSOCIATIVE PROPERTY OF SCALAR MULTIPLICATION

The scalar product of a real number, r, and a matrix A is the matrix rA. Each element of matrix rA is r times its corresponding element in A.