Square Roots of Matrices and Operators
If A is a positive-definite matrix or operator, then there exists precisely one positive definite matrix or operator B with B2 = A; we then define A1/2 = √A = B. In general matrices may have multiple square roots or even an infinitude of them. For example the 2×2 identity matrix has an infinity of square roots.
Read more about this topic: Square Root
Famous quotes containing the words square and/or roots:
“Rationalists, wearing square hats,
Think, in square rooms,
Looking at the floor,
Looking at the ceiling.
They confine themselves
To right-angled triangles.”
—Wallace Stevens (1879–1955)
“If church prelates, past or present, had even an inkling of physiology they’d realise that what they term this inner ugliness creates and nourishes the hearing ear, the seeing eye, the active mind, and energetic body of man and woman, in the same way that dirt and dung at the roots give the plant its delicate leaves and the full-blown rose.”
—Sean O’Casey (1884–1964)