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

LambdaMax(A)

# S4 method for LambdaMax
to_numeric(object, values)

# S4 method for LambdaMax
.domain(object)

# S4 method for LambdaMax

# S4 method for LambdaMax
validate_args(object)

# S4 method for LambdaMax
dim_from_args(object)

# S4 method for LambdaMax
sign_from_args(object)

# S4 method for LambdaMax
is_atom_convex(object)

# S4 method for LambdaMax
is_atom_concave(object)

# S4 method for LambdaMax
is_incr(object, idx)

# S4 method for LambdaMax
is_decr(object, idx)

## Arguments

A

An Expression or numeric matrix.

object

A LambdaMax object.

values

A list of arguments to the atom.

idx

An index into the atom.

## Methods (by generic)

• to_numeric(LambdaMax): The largest eigenvalue of A. Requires that A be symmetric.

• .domain(LambdaMax): Returns the constraints describing the domain of the atom.

• .grad(LambdaMax): Gives the (sub/super)gradient of the atom with respect to each argument. Matrix expressions are vectorized, so the gradient is a matrix.

• validate_args(LambdaMax): Check that A is square.

• dim_from_args(LambdaMax): The atom is a scalar.

• sign_from_args(LambdaMax): The sign of the atom is unknown.

• is_atom_convex(LambdaMax): The atom is convex.

• is_atom_concave(LambdaMax): The atom is not concave.

• is_incr(LambdaMax): The atom is not monotonic in any argument.

• is_decr(LambdaMax): The atom is not monotonic in any argument.

## Slots

A

An Expression or numeric matrix.