Matries Flashcards
Is this matrix a 2x3 or a 3x2
2x3
- It has two rows
- And three columbs
What is the trace of a matrix
The sum of all the entries on the diagonal of the matrix spanning from the top left to the bottom right of the matrix
What is the transpose of a matrix
- It means to interchange the rows and columbs of a matrix
- It is denoted by the matrix being to the power of T
What are the 3 major matrix laws
What is the rule to do with the output of matrix multiplication
- Multiplication can only be done if the number of columbs in the first matrix is the same as the number of rows in second
3x2 X 2x3 is possible and it gives a 2x2 output
What are the four bonus rules of matrix algebra
How to calculate the determinant of a matrix
What is a minor
A determinent composed of the elements of a matrix but where the row and columb of the minor for which we solve is ignored
What is vital to remember when calculating a matrix of cofactors
The alternating positive negative grid
What is the adjoint of a matrix
- The tranverse of a matrix of cofactors
- adjA = (C)^T
What are the four key properties of determinants
What is the key equation to do with inverses
Whats the key equation to allow for the finding of the inverse of a matrix
How do you translate a object with matricies
- Multiply each point of the object by the matrix
How do you rotate an object with matricies
- A special matrix of
- {cosθ -sinθ}
- {sinθ cosθ}
- This gives a counter clockwise rotation by angle θ
- If we replace the angle θ with -θ we get clockwise roation using matrix
- {cosθ sinθ}
- {-sinθ cosθ}
What is the rank of a matrix
- A way to see if the there is a solution to the equation: AX = B
- It is the largest square non singular submatrix
What does consistant and inconsitant mean
- A set of equations is said to be consistant if solutions to the equations can be found
- A set of equations is said to be inconsistant if no solutions can be found
How to find if solutions exist
- Compare the rank of the equation matrix and then the augmented matrix
- If rank of A = rank of Ab then the equations are solvable
- If rank of Ab > A: then no solution
Summary of Rank rules
What is the eigenvector equation
- Where λ is the eigenvalue
- x is the eigenvector
What is another key equation for eigenvectors and eigenvalues
