- class picos.expressions.exp_specnorm.SpectralNorm(x)¶
The spectral norm of a matrix.
This class can represent the spectral norm of a matrix-affine expression (real- or complex valued). The spectral norm is convex, so we can form expressions of the form
SpectralNorm(X) <= twhich are typically reformulated as LMIs that can be handled by SDP solvers.
If the normed expression is a matrix , then its spectral norm is
where denotes the largest eigenvalue of a matrix, and denotes the adjoint matrix of (i.e., the transposed matrix if is real-valued).
If is scalar, then reduces to the the absolute value (or modulus) .
If is scalar, then coincides with the Euclidean norm of .
x (ComplexAffineExpression) – The affine expression to take the norm of.
Return a constraint that the expression is upper-bounded.
Denote multiplication with another expression on the right.
Denote multiplication with another expression on the left.
- property x¶
Real expression whose norm equals that of the original expression.