Add identity matrix and check for eigenvalue

matrix.hpp

@@ -108,6 +108,22 @@ public:
   const matrix hermitian_conjugate() const {
     return this->transpose().conjugate();
   }
+  const matrix I() const {
+    matrix m = matrix(this->num_entries, this->entry_dimension);
+    for (long long i = 0; i < this->num_entries; i++) {
+      for (long long j = 0; j < this->entry_dimension; j++) {
+        if (i == j) {
+          m[i][j] = cnumber(1, 0);
+        } else {
+          m[i][j] = 0;
+        }
+      }
+    }
+    return m;
+  }
+  const bool is_eigenvalue(cnumber z) const {
+    return ((*this - (this->I() * z)).determinant() == 0);
+  }
   const bool is_hermitian() const {
     if (this->entry_dimension != this->num_entries)
       return false;