Maths C

• 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"

• 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.

• ┌ a₁₁ a₁₂ a₁₃ ┐
• └ a₂₁ a₂₂ a₂₃ ┘
• ┌ 9 2 5 ┐
• └ 8 7 2 ┘

That is a₁₂ refers to the element in row 1, column 2 (2). a₂₃ refers to the element in row 2, column 3 (2).

• 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}

• 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

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

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

• The number (ad-bc) 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

• The inverse of a matrice has to be used as a substitute for dividing matrices.
• It is determined by:
• 1/ad-bc[_-c^d_a^-b]

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

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

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

• Identity Matrix
• I
• Inverse of a Matrix
• A^-1
• Transpose of a Matrix
• A^T