Quantitative Methods II
Maths:
Chapter 1: Matrices and vectors
aij: number in the i-th row and j-th column
- We can multiply a matrix and a vector only if the number of columns of
the matrix is equal to the dimension of the vector.
- The product of 2 matrices can only be determined if the number of
columns of the first matrix equals the number of rows of the second one.
Chapter 2: Systems of Linear Equation
Standard form: system rearranged with all terms with a variable on the left
and constant terms on the right
- A system of linear equation has either no solutions, one solution or
infinitely many solutions.
- A solvable system of equation has a unique solution if there are no free
variables, and infinitely many solutions if there are.
Endogenous variable: a variable that is changed or determined by other
variables (dependent)
Exogenous variable: a variable whose value is determined outside the model
and is imposed on the model (independent)
Chapter 3: The Inverse Matrix
Determinant: ad-bc, with bigger matrices, use + - + - method
- The determinant of a matrix = the determinant of its transpose
- For two square matrices A and B of the same order, det(A + B) is
generally not equal to det A + det B
- For two square matrices A and B of the same order, it holds that det AB
= det A · det B
Chapter 4: Financial mathematics
Future value of a single amount: K*(1+r)t
Present value of a single amount: F*(1+r)-t
(The rest of the formulas are in the formula sheet)
Maths:
Chapter 1: Matrices and vectors
aij: number in the i-th row and j-th column
- We can multiply a matrix and a vector only if the number of columns of
the matrix is equal to the dimension of the vector.
- The product of 2 matrices can only be determined if the number of
columns of the first matrix equals the number of rows of the second one.
Chapter 2: Systems of Linear Equation
Standard form: system rearranged with all terms with a variable on the left
and constant terms on the right
- A system of linear equation has either no solutions, one solution or
infinitely many solutions.
- A solvable system of equation has a unique solution if there are no free
variables, and infinitely many solutions if there are.
Endogenous variable: a variable that is changed or determined by other
variables (dependent)
Exogenous variable: a variable whose value is determined outside the model
and is imposed on the model (independent)
Chapter 3: The Inverse Matrix
Determinant: ad-bc, with bigger matrices, use + - + - method
- The determinant of a matrix = the determinant of its transpose
- For two square matrices A and B of the same order, det(A + B) is
generally not equal to det A + det B
- For two square matrices A and B of the same order, it holds that det AB
= det A · det B
Chapter 4: Financial mathematics
Future value of a single amount: K*(1+r)t
Present value of a single amount: F*(1+r)-t
(The rest of the formulas are in the formula sheet)
