If Is an Orthonormal Set in an Inner Product

question 35

True/False

If
is an orthonormal set in an inner product space V, and
is a
orthogonal matrix, then
is also an orthonormal set in V.

---

Definitions:

Selective Breeding

The process of breeding plants or animals for specific genetic traits, aiming to produce offspring with desirable characteristics.

Fraternal Twin

Siblings who are born at the same time but developed from two separate eggs fertilized by two different sperm, genetically similar as typical siblings.

Range of Reaction

The concept that an individual’s genetic makeup establishes the range of possible responses to different environmental qualities.

Epigenetics

The study of changes in organism caused by modification of gene expression rather than alteration of the genetic code itself.