Matrices Flashcards
Adding and subtracting matrices
Done element by element (only for matching square matrices)
Matrix definition
an array of quantities with m columns and n rows
Multiplying matrices by a scalar
Scalar multiplies every quantity in the matrix
Condition for multiplying two matrices AB
Must conform:
A column n = B row n
AB=BA (T/F)
F although for certain types of matrices it is valid
Multiplying matrices
We do row * column, essentially dot product, overlap will be that position in the newly formed matrix
Square matrix
One with the same number of columns as rows
Transpose of a matrix
When we flip the columns to rows and rows to columns, denoted by A^T
Symmetric matrix
It is the same when you transpose it, A=A^T
Asymmetric/skew matrix
It is the opposite when you transpose it:
A=-A^T
Diagonal Matrix
Only non zero values in diagonal from top left to bottom right
Identity matrix
Diagonal of 1s from top right to bottom left, rest are all 0s.
Matrix equivalent of multiplying by 1
Lower triangular matrix
Top right corner above diagonal all 0s
Upper triangular matrix
Bottom left corner below diagonal is all 0s
Inverse matrices
A^-1,
A^-1A=I=AA^-1
