Free thyroxine (free T4) tests are used to help evaluate thyroid function and diagnose thyroid diseases, including hyperthyroidism and hypothyroidism, usually after discovering that the thyroid stimulating hormone (TSH) level is abnormal. T4 and another hormone called triiodothyronine (T3) are produced by the thyroid gland.
[When the determinant of a matrix is nonzero, linear system it represents is linearly independent]. When the determinant of a matrix is zero, it rows are linearly dependent vectors, and its columns are linearly dependent vectors.
An orthogonal matrix Q is necessarily invertible (with inverse Qâ1 = QT), unitary (Qâ1 = Qâ) and therefore normal (QâQ = QQâ) in the reals. The determinant of any orthogonal matrix is either +1 or â1. As a linear transformation, an orthogonal matrix preserves the dot product of vectors, and therefore acts as an isometry of Euclidean space, such as a rotation or reflection. In other words, it is a unitary transformation. The set of n Ã n orthogonal matrices forms a group O(n), known as the orthogonal group. The subgroup SO(n) consisting of orthogonal matrices with determinant +1 is called the special orthogonal group, and each of its elements is a special orthogonal matrix.