I am new to world of matrix, sorry for this basic question I could not figure out:
I have four matrix (one unknown).
Matrix X
x <- c(44.412, 0.238, -0.027, 93.128, 0.238, 0.427, -0.193, 0.673, 0.027,
-0.193, 0.094, -0.428, 93.128, 0.673, -0.428, 224.099)
X <- matrix(x, ncol = 4 )
Matrix B : need to be solved , 1 X 4 (column x nrows), with b1, b2, b3, b4 values
Matrix G
g <- c(33.575, 0.080, -0.006, 68.123, 0.080, 0.238, -0.033, 0.468, -0.006,
-0.033, 0.084, -0.764, 68.123, 0.468, -0.764, 205.144)
G <- matrix(g, ncol = 4)
Matrix A
a <- c(1, 1, 1, 1) # one this case but can be any value
A <- matrix(a, ncol = 1)
Solution:
B = inv(X) G A # inv(X) is inverse of the X matrix multiplied by G and A
I did not know how to solve this properly, particularly inverse of the matrix. Appreciate your help.
I'm guessing that Nick and Ben are both teachers and have even greater scruples than I do about doing other peoples' homework, but the path to a complete solution was really so glaringly obvious that it didn't make a lot of sense not to tae the next step:
B = solve(X) %*% G %*% A
> B
[,1]
[1,] -2.622000509
[2,] 7.566857261
[3,] 17.691911600
[4,] 2.318762273
The QR method of inversion can be invoked by supplying an identity matrix as the second argument:
> qr.solve(G, diag(1,4))
[,1] [,2] [,3] [,4]
[1,] 0.098084556856 -0.0087200426695 -0.3027373205 -0.0336789016478
[2,] -0.008720042669 4.4473233701790 1.7395207242 -0.0007717410073
[3,] -0.302737320546 1.7395207241703 13.9161591761 0.1483895429511
[4,] -0.033678901648 -0.0007717410073 0.1483895430 0.0166129089935
A more computationally stable solution is to use qr rather than solve.
method1 <- solve(X) %*% G %*% A
method2 <- qr.coef(qr(X), G) %*% A
stopifnot(isTRUE(all.equal(method1, method2)))
See the examples in ?qr.
来源：https://stackoverflow.com/questions/8065109/inverse-of-matrix-and-multiplication