DEFINITIONS DEALING WITH MATRICES...

Terms:	Definitions:
Matrix	A matrix is an ordered set of numbers listed in a rectangular form.
Matrix Theory	Numerous applications dealing with matrices.
Square Matrix	If a square matrix is when a matrix has the same number of rows as columns.
Row Matrix	A matrix with one row is called a row matrix
Column Matrix	A matrix with one column is called a column matrix
Scalars	Are real numbers.
Real Number	The union of rational and irrational numbers, any number besides infinite ones.
Vectors	matrices with only one row or column
Identity Matrix	When all the elements of a matrix A are 0,but a diagonal of 1's streching from the upper left to the lower right is present.
Inverse Matrix	If we change the sign of all the elements of a matrix A, we have the opposite matrix -A. If A' is the opposite of A
Matrices of the same size	Matrix A and B are of the same kind if and only if A has as many rows as B and A has as many columns as B.
Diagonal Matrix	The elements of a diagonal matrix are zero off the diagonal. An example is the matrix of regularisation parameters appearing in the equation for the optimal weight in local ridge regression
Matrix Equality	Two matrices are equal only if corresponding entries are equal.
0-Matrix	When all the elements of a matrix A are 0, we call A a 0-matrix. We write shortly 0 for a 0-matrix. An identity matrix I An identity matrix I is a diagonal matrix with all diagonal element = 1.
Augmented Matrix	A set of equations sharing the same variables may be written as an augmented matrix
Linear Equation	A Linear Equation is an equation of the form m * X + c = 0 where X is the unknown. The name "linear" stems from the fact that the graph of this equation is a straight line. If we plot a graph of mx + c we will see a straight line with a slope of m that intersects the y axis at y = c. Solving the equation means finding the value of x where the line intersects the x-axis.

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Latest update to this document: 16 November 2001

Jessica Schneider: jeschnei@nmu.edu