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NickHendo
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ORDER
 The number of rows and columns a matrice has. E.g. a matrix with m rows and n columns has an order of "m x n".
 HINT: Use the term "Remote Control  RC" to remember "Rows x Columns"

ELEMENTS
 An element in a matrice is any number located within that matrice.
 The elements of matrix A are reffered to as a_{ij} where 'i' is is the row position and 'j' is column position.
 ┌ a_{11} a_{12} a_{13} ┐
 └ a_{21} a_{22} a_{23} ┘
 ┌ 9 2 5 ┐
 └ 8 7 2 ┘
That is a _{12} refers to the element in row 1, column 2 (2). a _{23} refers to the element in row 2, column 3 (2).

COMFORMABLE
 If matrices are to be multiplied, they must be comformable.
 That is, the number of columns imn the first matrix must be the same as the number of rows in the second
 m x n x n x p = m x p
 ↑↑↑
 _{Must be the} _{same  Order of product}

IDENTITY MATRIX
 A matrix with all of its leading diagonal elements equal to 1.
 An identity matrix is denoted by I and acts in a similar fashion to the number 1.
 The leading diagonal is from top left to bottom right

COMMUTATIVE
 Addition of matrices is associative.
 That is, A + B = B + A
 Multiplication of matrices is NOT commutative.
 That is AB ≠ BA

ASSOCIATIVE
 Addition of matrices is associative.
 That is, (A + B) + C = A + (B + C)

DETERMINANT
 The number (adbc) is called the determinant and is written as detA or A
 If the determinant is = 0 then there is no inverse for that matrice as 1/0 is undefined

INVERSE
 The inverse of a matrice has to be used as a substitute for dividing matrices.
 It is determined by:
 1/adbc[_{c}^{d}_{a}^{b}]

TRANSITION
The transition matrix represents the probabilities that something will move from one state to another

SIMULTANEOUS
 Simultaneous
 ┌ a b ┐┌ x ┐= ┌4┐
 └ c d ┘└ y ┘= └5┘
 To solve, inverse of the first matix will need to be used

MARKOV CHAIN
A Markov chain is used to make predictions and long term forecasts based on current information

NOTATIONS
 Identity Matrix
 I
 Inverse of a Matrix
 A^{1}
 Transpose of a Matrix
 A^{T}

