User:Dcljr/Sandbox

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1 Glossary of matrix theory
2 Default wikitext for user pages
3 Multilingual monthly statistics by size
4 List of CPU flags

[edit] Glossary of matrix theory

The terms below are used in the branch of mathematics called matrix theory, which is often considered a subfield of linear algebra. For specific types of matrices, see the List of matrices. For some matrix operations, see Matrix.

Matrix

A rectangular array of objects which are usually members of a ring.

The definitions below will assume the following matrix:

$A = \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{bmatrix} = (a_{ij})_{i=1,\ldots,m \atop j=1,\ldots,n}$

Element: One of the objects in a matrix.; a_ij for a specific choice of i and j.

Size or dimensions: The number of rows and columns, respectively, of a matrix; usually expressed in the form m × n, read "m by n".

i-th row of matrix A: $\begin{bmatrix} a_{i1} & a_{i2} & \cdots & a_{in} \end{bmatrix}$

j-th column of matrix A: $\begin{bmatrix} a_{1j} \\ a_{2j} \\ \vdots \\ a_{mj} \end{bmatrix}$

Main diagonal: The elements whose row and column number match.; $\{a_{kk}:\,k = 1, \ldots, \min(m,n)\}$

Transpose: An operation resulting in a new matrix whose rows are the columns of the original matrix and whose columns are the rows of the original matrix, or the resulting matrix itself.; $A^T = (a_{ji})_{i=1,\ldots,m \atop j=1,\ldots,n}$

Trace: The sum of the elements on the main diagonal.; $\mbox{tr}\,A = a_{11} + a_{22} + \ldots + a_{kk}, \mbox{ where } k=\min(m,n)$

...

Minor: The determinant of the matrix obtained by deleting a given row and column from the original matrix.; $M_{ij}=\begin{vmatrix} a_{11} & \cdots & a_{1,j-1} & a_{1,j+1} & \cdots & a_{1n} \\ \vdots & & \vdots & \vdots & & \vdots \\ a_{i-1,1} & \cdots & a_{i-1,j-1} & a_{i-1,j+1} & \cdots & a_{i-1,n} \\ a_{i+1,1} & \cdots & a_{i+1,j-1} & a_{i+1,j+1} & \cdots & a_{i+1,n} \\ \vdots & & \vdots & \vdots & & \vdots \\ a_{m1} & \cdots & a_{m,j-1} & a_{m,j+1} & \cdots & a_{mn} \end{vmatrix}$; Note that the i-th row and j-th column are missing in the above determinant.

...

Vector: A matrix with one row (a row vector) or one column (column vector).; See Vector for more information.

Linear transformation: The function that results from multiplying a given matrix by an appropriately sized vector of variables.; $f:\mathbb{R}^n\to\mathbb{R}^m,\mbox{ where }f(x)=Ax,\ x\in\mathbb{R}^n.$

Rank: The dimension of the space generated by the rows of a given matrix.; The dimension of the image of the linear transformation represented by the matrix.

[edit] Default wikitext for user pages

Default wikitext for user pages on non-English wikis:

'''dcljr''' is a [[:en:Mathematics|math]] [[:en:Tutor|tutor]] ([[tutor]]) who lives in
[[:en:Austin, Texas|Austin, Texas]] ([[Austin, Texas]]; [[Austin]], [[Texas]]).

Sorry, I don't speak [[:en:FOO language|FOO]].
My native language is [[:en:English language|English]].
([[:en:User:Dcljr]])
----
This Wikipedia contains {{NUMBEROFARTICLES}} articles. (See the
[[Special:Newpages|newest articles]] or [[Special:Recentchanges|recent changes]].)

[edit] Multilingual monthly statistics by size

See Wikipedia:Multilingual monthly statistics.

[edit] List of CPU flags

de, DE - ???
fpu, FPU - Floating point unit (FPU redirects to)
msr, MSR - model-specific register / model specific register or machine-specific register / machine specific register? (see Processor register)
pae, PAE - Physical Address Extension
cx8, CX8 - ???
apic, APIC - IO-APIC (I/O Advanced Programmable Interrupt Controller)
cmov, CMOV - ???
fxsr, FXSR - "FX* instructions"?? (see 3DNow!)
mca, MCA - Micro Channel architecture
mmx, MMX - Matrix Math Extensions / Matrix Math Extension (see also x86, SIMD)
mmext, MMEXT - ?
mp, MP - ???
mtrr, MTRR - Memory Type Range Registers / Memory Type Range Register (see MTRR)
pat, PAT - Performance acceleration technology?
pge, PGE - ???
psa, PSA - ???
pse36, PSE36 - ???
sep, SEP - ???
sse, SSE - Streaming SIMD Extensions (see also x86, SIMD)
syscall, SYSCALL - System call
3dnow, 3DNOW - 3DNow! (see also x86, SIMD)
3dnowext, 3DNOWEXT - Enhanced 3DNow!?
tsc, TSC - Time Stamp Counter (see TSC page)
vme, VME - VMEbus??

others: acpi/ACPI, clflush/CLFLUSH, dts/DTS, ht/HT, mce/MCE, ss/SS, sse2/SSE2, sse3/SSE3, tm/TM

what about: AVR instruction set?, Register Transfer Language?

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User:Dcljr/Sandbox

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