Matrix
The Transformation given by the system of equations
 |  |  | |
 | |  | |
 | |||
 | |  |
is denoted by the Matrix Equation
In concise notation, this could be written
where
and 
are Vectors and A is called an 
matrix. A matrix is said tobe Square if 
. Special types of Square Matrices include theIdentity Matrix 
, with 
(where 
is the Kronecker Delta) and theDiagonal Matrix 
(where 
are a set of constants).For every linear transformation there exists one and only one corresponding matrix. Conversely, every matrix corresponds to aunique linear transformation. The matrix is an important concept in mathematics, and was first formulated bySylvester 
and Cayley.
Two matrices may be added (Matrix Addition) or multiplied (Matrix Multiplication) together to yield a newmatrix. Other common operations on a single matrix are diagonalization, inversion (Matrix Inverse), and transposition(Matrix Transpose). The Determinant 
or 
of a matrix A is a very importantquantity which appears in many diverse applications. Matrices provide a concise notation which is extremely useful in a widerange of problems involving linear equations (e.g., Least Squares Fitting).
References
Arfken, G. ``Matrices.'' §4.2 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 176-191, 1985.
- Catastrophe
- Catastrophe Theory
- Categorical Game
- Categorical Variable
- Category
- Category Theory
- Catenary
- Catenary Evolute
- Catenary Involute
- Catenary Radial Curve
- Catenoid
- Caterpillar Graph
- Cat Map
- Cattle Problem of Archimedes
- Cauchy Binomial Theorem
- Cauchy Boundary Conditions
- Cauchy Criterion
- Cauchy Distribution
- Cauchy Equation
- Cauchy Functional Equation
- Cauchy-Hadamard Theorem
- Cauchy Inequality
- Cauchy Integral Formula
- Cauchy Integral Test
- Cauchy Integral Theorem