It is well known that any operation on a quantum computer is described with a unitary matrix (a quantum gate) because quantum computing is reversible.
Only non-reversible operation is a measurement of a qubit. Therefore, I would expect that the measurement can be described by a non-unitary matrix (or even by matrix that is not invertible).
A result of the measurement should be a probability distribution of all possible states of measured qubits.
My question: How does a matrix representing measurement of qubit(s) look like?