Mathematics and Computation Flashcards
What is a matrix with only one dimension?
a vector
What is a matrix?
a 2d array of numbers
m(rows) X n(columns)
How do you find an element within a matrix?
element denoted by A¬ij where i is the row and j is the column
How do you enter row and columns is matlab?
use commas for rows and semi colons for columns
How do you access a matrix element in matlab?
A(i, j) returns A¬ij
How do you access the whole row or column in matlab?
use a colon in place of row or column
How do you access part of a matrix row or column in matlab?
use X:Y, shows numbers X to Y (inclusive)
How do you find how many rows or columns a matrix has in matlab?
size(M) shows both
size(M, 1) shows rows
size(M, 2) shows columns
How do you add matrices?
they have to be the same size and just add the numbers that are in the same spot
How do you subtract matrices?
matrices have to be the same size and just subtract the numbers that are in the same spot
How do you do scalar multiplication of matrices?
multiply each of the elements by the scalar value
What does transposing a matrix do?
flips the matrix diagonally
m x n -> n x m
How do you transpose a matrix in matlab?
Transpose(A)
What is a diagonal matrix?
the elements where the row and column are the same and the rest are zeros
What is the trace of a matrix?
the sum of all the elements on the diagonal
How do you trace in matlab?
trace(A)
How do you make a zero matrix in matlab?
zeros(m, n)
What is an identity matrix?
a diagonal matrix containing only 1’s
How do you make an identity matrix in matlab?
eye(n) == n x n identity matrix
How can a matrix be symmetric?
when A = Transpose(A)
How can a matrix be skew symmetric?
when A = -Transpose(A)
only happen when diagonal elements are 0
What is a triangular matrix?
when all the elements are 0 above(lower) or below(upper) the diagonal
How do you divide a matrix?
multiply by the reciprocal
What does sum() do in matlab?
if the matrix is a vector it will add all the elements, if it is a matrix is will sum the values of each column
What does prod() do in matlab?
if the matrix is a vector it will multiply all the elements, if it is a matrix it will multiply the values of each column
What does mean() do in matlab?
if the matrix is a vector it will mean all the elements, if it is a matrix it will mean the values of each column
What does sqrt() do in matlab?
it square roots each of the values in the matrix
What does “.” mean in matlab?
means to process each element of the matrix independently of the others
What does plot(X, Y) mean in matlab?
it plots a line using the coordinates in X and Y
How do you put multiple lines on one graph?
Either put it in one plot function or type “hold on” to add it to the same graph, type “hold off” to stop
How to do element wise operations in matlab?
put a “.” and then the operation
What is the condition of matrix multiplication?
the number of columns in the first must equal the number of rows in the other
What will the rows and columns be after matrix manipulation?
the rows of the first one and the columns of the other
What is the product of transpose(AB) equal?
transpose(B) x transpose(A)
How do you denote vectors?
usig a bold lower case letter
What does diag() do in matlab?
makes a column vector of the diagonal element of a matrix
How do you solve simultaneous equations using matrices?
put into form [ numbers ] [ x = [ ans ]
y ]
then times by matrix that when times by the numbers it creates a 0 on the bottom left and top right
How do you solve simultaneous equations using magic matrix in matlab?
mA = MA; mb = Mb
mb./diag(mA)
How do you scale using matrix multiplication?
add 1s to the bottom of the matrix to make it a 3xn matrix then times by [ Sx 0 0
0 Sy 0
0 0 0 ]
How do you rotate using matrix multiplication?
add 1s to the bottom of the matrix to make it a 3xn matrix then times by [ cosx -sinx 0
sinx cosx 0
0 0 0 ]
How do you translate using matrix multiplication?
add 1s to the bottom of the matrix to make it a 3xn matrix then times by [ 1 0 Tx
0 1 Ty
0 0 1 ]
How do you combine scale and rotation in matrix multiplication?
times them together right to left
How do you define the coordinates of a shape in matlab?
start at one point and go round until you input the first one again
How do you change the base of a log?
log a (X) = (log b (X) / log b (a))
What is a sigmoid function?
a smooth transition from 0 to 1
What is a tanh function?
smooth transition from -1 to 1
How can a phase shifted sinusoid be expressed using sin and cos?
Ksin(ωt + 𝜙) = Ksin(ωt)cos(𝜙) + Kcos(ωt)sin(𝜙)
How do you find 𝜙 of phase shifted sinusoid?
if x = 0 and y > 0 𝜙 = π/2
if x = 0 and y < 0 𝜙 = -π/2
if x > 0 𝜙 = arctan(y/x)
if x < 0 and y ≥ 0 𝜙 = arctan(y/x)+π
if x < 0 and y < 0, 𝜙 = arctan(y/x) − π
How do you create a variable that increments in matlab?
starting value: increment: end value
How can you have many graphs on one figure in matlab?
use subplot(x,y, p)
x and y is how many on x and y axis then p is the position reading like a book
How do you use multiple figures in matlab?
figure(number)
How do you differentiate polynomials in matlab?
polyder(coefficients to the equation)
How do you intergrate in matlab?
polyint(coefficients to the equation)
How do you evaluate a polynomial in matlab?
polyval(polynomial coefficients, number entered)
What is the inverse of matrix A?
the adjoint of A / the determinant of A
How do you find the cofactor?
cross out the row and column of that cofactor and is it positive if i+j is even and opposite
How do you find the determinant of a matrix?
a11C11 + a12C12 and so on
How do you find the adjoint of a matrix?
Transpose[c11, c12;c21, c22]
What is Cramer’s rule?
find variables of [x1;x2;…]
xk = Dk/D
where Dk is the determinants of D where the kth column is replaced by b
How do you find the inverse of a diagonal matrix?
1 over values in the diagonal
