Maximum Eigenvalue

The maximum eigenvalue of a matrix, \(\lambda_{\max}(A)\).

lambda_max(A)

Arguments

A

An Expression or matrix.

Value

An Expression representing the maximum eigenvalue of the input.

Examples

A <- Variable(2,2)
prob <- Problem(Minimize(lambda_max(A)), list(A >= 2))
result <- solve(prob)
result$value
#> [1] 4
result$getValue(A)
#>      [,1] [,2]
#> [1,]    2    2
#> [2,]    2    2

obj <- Maximize(A[2,1] - A[1,2])
prob <- Problem(obj, list(lambda_max(A) <= 100, A[1,1] == 2, A[2,2] == 2, A[2,1] == 2))
result <- solve(prob)
result$value
#> [1] 0
result$getValue(A)
#>      [,1] [,2]
#> [1,]    2    2
#> [2,]    2    2