Erratum to “Ranks of a Constrained Hermitian Matrix Expression with Applications”

---

The equalities (15) and (16) should be deleted from Lemma 3 which will be reformatted as follows.

Lemma 3. Let 𝐴=𝐴^∗∈ℍ^𝑚×𝑚, 𝐵∈ℍ^𝑚×𝑛, and 𝐶∈ℍ^𝑝×𝑚 be given. Assume that ℛ(𝐵)⊆ℛ(𝐶^∗). Then,

max_𝑋𝑟𝐴−𝐵𝑋𝐶−(𝐵𝑋𝐶)^∗=min𝑟𝐴𝐶^∗𝐵,𝑟𝐴𝐵_∗0,min_𝑋𝑟𝐴−𝐵𝑋𝐶−(𝐵𝑋𝐶)^∗=2𝑟𝐴𝐶^∗𝐵+𝑟𝐴𝐵_∗0−2𝑟.𝐴𝐵𝐶0 (17)