Matrices Flashcards
How do you write the dimensions of a matrix?
Row X Column
What is a square matrix?
A matrix is a square if it has the same number of rows as columns
What is a zero matrix?
A zero matrix is one in which all the elements are 0
What is an identity matrix?
An identity matrix is a square matrix which as 1’s In the ‘leading diagonal’ and 0 elsewhere
What the properties of matrix multiplication?
Matrix multiplication is associative but not commutative
What dictates for two matrices can be multiplied?
They multiply if P x Q *** Q x P
What type of matrices can be raised to a power?
Square Matrices
What is a linear transformation?
T(ka) = kT(x)
(kb) (y)
T(a + b) = T(a) + T(b)
What does i- and j- represent?
i- = (1) and j- = (0)
(0) (1)
How could a matrix transformation be represented in terms of i- and j-?
( T[i] T[j] )
Where ‘T’ is the transformation of ‘I’ and ‘j’
What matrix represents an enlargement of SF ‘k’?
(k 0)
(0 k)
What matrix represents a rotation of ‘x’ anticlockwise?
(cos x -sinx)
( )
(sin x cosx)
This is an ANTICLOCKWISE rotation
What is a shear transformation?
A shear transformation is when one direction is changed and the other stays the same
What is the matrix for a stretch of scale factor ‘k’ parallel to the x axis?
(k 0)
(0 1)
What is the matrix for a stretch of scale factor ‘k’ parallel to the y axis?
(1 0)
(0 k)
What is the matrix for a shear with a fixed x axis?
(1 k)
(0 1)
What is the matrix for a shear with a fixed y axis?
(1 0)
(k 1)
What is the formula for the shear factor?
Distance between a point and its image///Distance between original point and x-axis = SF
How do you calculate the combined transformation for B and then A?
Matrix A *** Matrix B
It is always the second one multiplied by the first one
What are the dimensions of the matrix for 3D transformations?
3x3
What do i-, j-, and k- equal?
i* = (1) j* = (0) k* = (0)
(0) (1) (0)
(0) (0) (1)
What is the matrix for a reflection in the plan z = 0?
(1 0 0)
(0 1 0)
(0 0 -1)
What is the matrix for a reflection in the plan x = 0?
(-1 0 0)
(0 1 0)
(0 0 1)
What is the matrix for a reflection in the plan y = 0?
(1 0 0)
(0 -1 0)
(0 0 1)
What is the matrix for a rotation ‘x’ degrees anticlockwise about the y axis?
(cosx 0 sinx)
(0 1 0)
(-sinx 0 cosx)
What is the matrix for a rotation ‘x’ degrees anticlockwise about the x axis?
(1 0 0)
(0 cosx -sinx)
(0 sinx cosx)
What is the matrix for a rotation ‘x’ degrees anticlockwise about the z axis?
(cosx -sinx 0)
(sinx cosx 0)
(0 0 1)
