Matrices properties Flashcards
For matrices defined as:
- A n×m
- B m×j
- C j×k
What is the associativity property for (AB)C?
(A·B)·C = A·(B·C)
This allows us to group matrices differently without changing the result.
For matrices defined as:
- A n×m
- B m×j
- C m×j
What is the distributivity property for A(B + C)?
A·(B + C) = AB + AC
For matrix defined as:
- A n×m
What will Im·A be equal to ?
A
because the identity matrix doesn’t affect the matrices it is multiplied to
What is the identity matrix
A martix that has only ones in its diagonal and zeros everywhere else
e.g. :
[1,0,0]
[0,1,0]
[0,0,1]
If a matrix has a matrix inverse, give 3 properties of it
- Regular
- Non singular
- Invertible
If a matrix doesn’t have a matrix inverse, give 2 properties of it
- Singular
- Non invertible
If A-1 exists, it is ..?
Unique
How do you find A-1
( 1 / determinant (A) ) x Adjoint(A)
A · A-1 = ?
A-1 · A
(A · B)-1 = ?
B-1 · A-1
is the statement true ?
(A + B)-1 = A-1 + B-1
NO
(AT)T = ?
A
(A + B)T = ?
AT + BT
(A · B)T = ?
BT · AT
A is symetric if ..?
A = AT
What is the only type of matrices than can be symetric ?
N x N matrices (also called square matrices)
If A-1 exists, what does it tells us about A-T
It tells us that A-T also exists
Is the sum of symetric matrices also always symetric ?
Yes
Is the product of symetric matrices also always symetric ?
No but it is always defined
for (x,y) ℝ, and C n×m
is the statement true:
(xy)C = x(y · C)
Yes
for (x,y) ℝ, and Bn×m Cm×j
is the statement true:
x(B · C) = B(x · C)
Yes
for (x,y) ℝ, and Cn×m
is the statement true:
(xy) · C = xC · yC
Yes
for (x,y) ℝ, and Bn×m Cm×j
is the statement true:
x(B + C) = xB + xC
Yes
