Combinatory logic: Difference between revisions

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In [[linear algebra]], a '''column vector''' or '''column matrix''' is an ''m'' &times; 1 [[matrix (mathematics)|matrix]], i.e. a matrix consisting of a single column of ''m'' elements.
 
:<math>\mathbf{x} = \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_m \end{bmatrix}</math>
 
The [[transpose]] of a column vector is a [[row vector]] and vice versa:
 
:<math>\begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_m \end{bmatrix}^{\rm T} = \begin{bmatrix} x_1 \; x_2 \; \dots \; x_m \end{bmatrix}</math>
 
The set of all column vectors with a given number of elements forms a [[vector space]] which is the [[dual space]] to the set of all row vectors with that number of elements.
 
== Notation ==
To simplify writing column vectors in-line with other text, sometimes they are written as row vectors with the transpose operation applied to them.
 
:<math>\mathbf{x} = \begin{bmatrix} x_1 \; x_2 \; \dots \; x_m \end{bmatrix}^{\rm T}</math>  
:or
:<math>\mathbf{x} = \begin{bmatrix} x_1, x_2, \dots, x_m \end{bmatrix}^{\rm T}</math>
 
For further simplification, some authors also use the convention of writing both column vectors and row vectors as rows, but separating row vector elements with [[comma]]s and column vector elements with [[semicolon]]s (see alternative notation 2 in the table below).  
 
{| class="wikitable"
|-
! !! Row vector !! Column vector
|-
| '''Standard matrix notation'''
| align=center| <math> \begin{bmatrix} x_1 \; x_2 \; \dots \; x_m \end{bmatrix} </math>
| align=center| <math> \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_m \end{bmatrix} \text{ or } \begin{bmatrix} x_1 \; x_2 \; \dots \; x_m \end{bmatrix}^{\rm T} </math>  
|-
| '''Alternative notation 1'''
| align=center| <math> \begin{bmatrix} x_1, x_2, \dots, x_m \end{bmatrix} \qquad </math>
| align=center| <math> \begin{bmatrix} x_1, x_2, \dots, x_m \end{bmatrix}^{\rm T} </math>
|-
| '''Alternative notation 2'''
| align=center| <math> \begin{bmatrix} x_1, x_2, \dots, x_m \end{bmatrix} \qquad </math>
| align=center| <math> \begin{bmatrix} x_1; x_2; \dots; x_m \end{bmatrix} </math>
|}
 
== Operations ==
* [[Matrix multiplication]] involves the action of multiplying each row vector of one matrix by each column vector of another matrix.  
 
* The [[dot product]] of two vectors '''a''' and '''b''' is equivalent to multiplying the row vector representation of '''a''' by the column vector representation of '''b''':
 
:<math>\mathbf{a} \cdot \mathbf{b} = \mathbf{a}^\mathrm{T} \mathbf{b} = \begin{bmatrix}
    a_1  & a_2  & a_3
\end{bmatrix}\begin{bmatrix}
    b_1 \\ b_2 \\ b_3
\end{bmatrix}.</math>
 
== See also ==
* [[Covariance and contravariance of vectors]]
 
== References ==
{{see also|Linear algebra#Further reading}}
* {{Citation
| last = Axler
| first = Sheldon Jay
| date = 1997
| title = Linear Algebra Done Right
| publisher = Springer-Verlag
| edition = 2nd
| isbn = 0-387-98259-0
}}
* {{Citation
| last = Lay
| first = David C.
| date = August 22, 2005
| title = Linear Algebra and Its Applications
| publisher = Addison Wesley
| edition = 3rd
| isbn = 978-0-321-28713-7
}}
* {{Citation
| last = Meyer
| first = Carl D.
| date = February 15, 2001
| title = Matrix Analysis and Applied Linear Algebra
| publisher = Society for Industrial and Applied Mathematics (SIAM)
| isbn = 978-0-89871-454-8
| url = http://www.matrixanalysis.com/DownloadChapters.html
}}
* {{Citation
| last = Poole
| first = David
| date = 2006
| title = Linear Algebra: A Modern Introduction
| publisher = Brooks/Cole
| edition = 2nd
| isbn = 0-534-99845-3
}}
* {{Citation
| last = Anton
| first = Howard
| date = 2005
| title = Elementary Linear Algebra (Applications Version)
| publisher = Wiley International
| edition = 9th
}}
* {{Citation
| last = Leon
| first = Steven J.
| date = 2006
| title = Linear Algebra With Applications
| publisher = Pearson Prentice Hall
| edition = 7th
}}
 
[[Category:Linear algebra]]
[[Category:Matrices]]
[[Category:Vectors]]

Latest revision as of 19:08, 21 November 2014

If the BMI examination result is in merely 18.5 - 24.nine, it may be thought to be usual. What this means is that the particular person is balanced however, nevertheless should observe appropriate diet program and exercise to keep about being in superior shape. Although the BMI suggests a healthful system, undergoing an yearly bodily verify up remains to be critical.



Due to the fact a better program fat is connected with many illnesses like heart health problems, diabetic issues plus several types of cancer to name a number of, giving a numeric importance to an individual's body fat composition can be a fair guidebook to problems caused by excessive fat. Although it's a manual, it is just which and should be selected right into element with other elements compared to only simply the BMI amount value.

James Laska has been associated with different health centers. The writer is a personality who has wise knowledge regarding many diet tools plus programs and also weight losing medications.For More Information Please Visit,calories burned while walking & Weight Loss Center.

BMI, that stands for "body-mass index", is an extremely popular measure for weight. It certainly is calculated by taking your fat inside kilos and dividing it by the square of the height in metres. It is additionally acknowledged because the Quetelet Index, after its Belgian founder. It is used about the world by several governments inside their official wellness requirements. Uncover out a small bit more about the BMI and certain objections inside opposition to generating use of this usual standard.

Patients who are categorized beneath the underweight ranking have just as much of the possibility of developing wellness issues because those that fall beneath the overweight and overweight categories. It only more popular to find an overweight individual with wellness programs than an underweight.

Measuring a person's waist circumference puts most 'dislikers' of the BMI (see above)at ease because it enables a more exact measuring of the person's body fat. If a muscular individual is rated because obese found on the BMI, measuring their waist circumference will determine if that individual is indeed obese.

If the calculator happen shows BMI happen between 18.5- 24.9, then it signifies that you have a healthy weight plus you do not need to do something additional.

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