List of matrices
Listed below are some important classes of matrices used in mathematics:
- Diagonal matrix - All entries not on the main diagonal (the diagonal from the upper left to the lower right corner) are zero. Especially easy to raise to a power.
- Diagonalizable matrix - A matrix similar to a diagonal matrix. It has a complete set of linearly independent eigenvectors.
- Normal matrix - It has a complete set of orthonormal eigenvectors.
- Symmetric matrix - A matrix that is its own transpose.
- Hermitian matrix - A matrix that is its own conjugate transpose. It is a normal matrix.
- Positive definite matrix - Hermitian matrix with every eigenvalue positive.
- Orthogonal matrix - A matrix which has the same inverse and transpose, can represent a rotation.
- Unitary matrix - A matrix whose conjugate transpose is its inverse.
- Positive matrix[?] - A matrix with all numbers ≥ 0.
- Totally positive matrix[?] - Determinants of all its square submatrices are positive. It is used in generating the reference points of Bézier curve in computer graphics.
- Stochastic matrix - A positive matrix describing a stochastic process. The sum of entries of any row is one.
- Permutation matrix - Matrix representation of a permutation.
How happy were I then!
LUCIFER. thou.html">thou.html">thou.html">Thou shalt; I will send for thee at midnight.<110>
And thou shalt turn thyself into what shape thou wilt.
FAUSTUS. Great thanks, mighty Lucifer!
[Exeunt LUCIFER and BELZEBUB.]
Come, Mephistophilis.
To know the secrets of astronomy<112>
Did mount himself to scale Olympus' top,
Drawn by the strength of yoky dragons' necks.
And, as I guess, will first arrive at Rome,
And take some part of holy Peter's feast,
[Exit.]
Enter FAUSTUS and MEPHISTOPHILIS.<113>
FAUSTUS. Having now, my good Mephistophilis,
Environ'd round with airy mountain-tops,
Not to be won by any conquering prince;
We saw.html">saw the river Maine fall into Rhine,
Then up to Naples, rich Campania,
The streets straight forth, and pav'd with finest brick,
There saw we learned Maro's golden tomb,
Thorough a rock of stone, in one night's space;
In one of which a sumptuous temple stands,<117>
Thus hitherto hath Faustus spent his time:
Hast thou, as erst I did command,
I have taken up his Holiness' privy-chamber for our use.
FAUSTUS. I hope his Holiness will bid us welcome.
MEPHIST.
And now, my Faustus, that thou mayst perceive
Know that this city stands upon seven hills
Just through the midst<118> runs flowing Tiber's stream
Over the which four stately bridges lean,
Upon the bridge call'd Ponte<119> Angelo
Within whose walls such store of ordnance are,
As match the days within one complete year;
Which Julius Caesar brought from Africa.
FAUSTUS. Now, by the kingdoms of infernal rule,
.
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