What is Matrix algebra: Definition and 65 Discussions
In abstract algebra, a matrix ring is a set of matrices with entries in a ring R that form a ring under matrix addition and matrix multiplication (Lam 1999). The set of all n × n matrices with entries in R is a matrix ring denoted Mn(R) (alternative notations: Matn(R) and Rn×n). Some sets of infinite matrices form infinite matrix rings. Any subring of a matrix ring is a matrix ring. Over a rng, one can form matrix rngs.
When R is a commutative ring, the matrix ring Mn(R) is an associative algebra over R, and may be called a matrix algebra. In this setting, if M is a matrix and r is in R, then the matrix rM is the matrix M with each of its entries multiplied by r.
Homework Statement
A range of metallic alloys are tested for electrical conductivity and give the following results for identically sized samples.
25% copper with 75% tin gave a reading of 0.0071 Ohms
65% copper with 35% cadmium gave a reading of 0.0049 Ohms
40% copper with 40% tin...
Homework Statement
If A is an nxn matrix such that A^3 = 0 (the zero matrix) then (I-A)^-1 = ...?
A. not invertible
B. I+A^2
C. I-A
D. I+A
E. I+A+A^2
Homework Equations
The Attempt at a Solution
I just don't know how to work out what the inverse of (I-A) is if I know A^3... how is this...
Homework Statement
Find a vector w in R3 such that w is not a linear combination of v1 and v2
Homework Equations
v1 = [1;2;-1] v2=[2;-1;-2]
The Attempt at a Solution
my question is : does w need to be in the span of v1 and v2?? Could i just choose [1; 1; 1] as my w vector??
1. Show that if a square matrix A satisfies A2 - 3A + I = 0, then A-1 = 3I - A
2. A-1A = I and A-1A = I and more that I can't think of
3. 3A = A2 + I
A = (A2 + I)/3
?
This question is weird :o
Anyone know how to do it?
Well I'm going to be taking Matrix Algebra next semester, and I have no clue what it's for. Wikipedia wasn't too enlightening. What is the purpose of matrix algebra, and what is is commonly used for?
Homework Statement
Hey, I need to decode a message hidden in a Matrix as a practice activity, and I'm rather stuck.
The alphabet key is starting from the letter A,numbered using first:
a)Fibonacci Sequence
b)Prime Numbers
c)Counting Numbers
d)No numbers higher than 27...
Homework Statement
Let a_1,...,a_n be Real. Then define a 2n x 2n matrix A as follows.
The following are the first 4 and the last 2 columns;
note that the (2k) column equals (a_k)(derivative of the (2k-1) column
A[,1] = a_1^(2n),a_1^(2n-1),a_1^(2n-2),...,a_1^(2), a_1
A[,2] =...
Homework Statement
Is the following true for matrices?
Hypotesis:
AB = AC
A != 0(zero matrix)
Thesis:
B=C
The Attempt at a Solution
AB = AC
AB - AC = 0(zero matrix)
AB - AC = A(B-C) // using the following property: A(B+C) = AB + AC iff A is mn matrix and BC are np matrices...
Hi,
We recently started analyzing linear machines using matrix algebra. Unfortunately, I haven't had much exposure to operating in finite fields aside from the extreme basics (i.e. the definitions of GF(P)). I can get matrix multiplication/addition, etc. just fine, but it's when finding the...
Homework Statement
On page 44 of Ryder's QFT, near the bottom of the page, it says:
Homework Equations
Equation (2.94) is
(\gamma^{\mu}p_{\mu} - m)\psi(p) = 0
The Attempt at a Solution
Writing out all four components, and then taking the determinant and setting to zero, I get:
m^4 - (E^2 -...
Homework Statement
This is from Ryder's QFT book, second ed. page 37. At the bottom of the page it says that the commutation relations (eqn 2.68?) are satisfied by:
K = \pm i\frac{\sigma}{2}
However, I do not find this to be so. What am I missing?
Homework Equations
Here is one of the...
A=(5, 4) I (1, 0)
(4,6) (0,1)
Those are matrix by the way.
How do I show A^2=11A-18I? I know I'm overlooking something, but i don't know what. Any tips would be helpful
Hi.
Marix A=
|1 1 0 |
|0 2 0 |
|2 1-1 |
Has three eigenvectors [1,1,1]^T, [1,0,1]^T and [0,0,1]^T, By using this knowledge solve A^11.
Ok, solving A^11 is rather easy with any decent calculator, or even with pen , paper and some time, but how on Earth I'm supposed to benefit...