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The '''[[row space]] and [[column space]]''' of an ''m''-by-''n'' [[matrix (mathematics)|matrix]] are the [[linear subspace]]s generated by row vectors and column vectors, respectively, of the matrix. Its [[Hamel dimension|dimension]] is equal to the [[Rank (linear algebra)|rank]] of the matrix and is at most min(''m'',&#8239;''n'').<ref>http://www.cliffsnotes.com/WileyCDA/CliffsReviewTopic/Row-Space-and-Column-Space-of-a-Matrix.topicArticleId-20807,articleId-20793.html</ref>
BMI Basics: The Body Mass Index is practical as a ballpark measuring. Health experts and organizations like the WHO, employ it to gain a standard idea of whether a individual is overweight, underweight, or is at a healthy weight, provided their height. If you're my age (which I'm not going to disclose,) we were possibly introduced to the BMI inside Middle School during PE. Back then I was taught to measure my BMI with a simple formula. A few punches found on the calculator plus voila, my body fat was quantified.<br><br>Free resource which you do not have to cognise how to puzzle out the [http://safedietplans.com/bmi-chart bmi chart]. The online tool does it for you. In order to do that you can choose some of the charts on this page. It won't take much time.<br><br>This way uses body fat scales which send a secure small bmi chart men electrical current by the body to calculate the amount of body fat tissue. Your body fat percentage is then calculated based on height, weight, age plus sex. It is a harmless method plus very exact. These scales are obtainable in the market and affordable.<br><br>Anorexia nervosa is an psychological disorder where the leading focus may be on food / the avoidance of food however it additionally deals with harmful methods of gaining perfection and a desire to control aspects. In a society that associates unreasonable thinness with beauty, there has been a marked escalation inside the amount of young adolescent women with anorexia. Many of them die due to starvation-related causes, suffer from bodily problems, or end up committing suicide. It is important to treat such people with psychotherapy, family therapy, and medication.<br><br>Besides the obvious weight and BMI measurements, you might wish to consider finding a model that has separate methods for male plus woman consumers. Weight distribution for people are different and scales which have a gender option might offer more exact readings.<br><br>I would like to share several insights plus tricks which bmi chart women I have learned along the method. Many of these women's running tips may apply to all runners, nevertheless they certainly take on a new perspective because the years go on plus you get elder, wiser, plus perhaps, quicker...<br><br>Obesity is not a single problem. There are several effects of weight. One of the initially plus foremost effects is inability to carry out day-to-day escapades. An fat individual is usually inactive and feels fatigued most of the time. Obesity gives birth to additional wellness issues. Some overweight persons develop Pickwick syndrome inside that a person feels drowsy plus color of his face remains reddish. Pain inside joints, bones, plus lower back part of the body is usually experienced by over-weight persons. Another chronic wellness issue which 1 can is susceptible to is diabetes that is incurable.<br><br>There is another method of calculating BMI for female in the event you do not want to convert feet and pounds to meters and kilograms. Take the earlier illustration of the woman weighing in at 150 pounds. Take the pounds that are 150 and instances it by 4.88 giving we 732, then derive the woman's height inside feet squared that is (5.5 occasions 5.5) that is 30.25 feet squared. Then hold on to these 2 results you merely got. Right after that, divide the weight by the height squared, in this case it would be (732 divided by 30.25) and the result is 24.1 that is really close to the earlier metric formula's outcome. See how simple it is very with regards to BMI calculations for women!
 
The rest of article will consider matrices of [[real number]]s: row and column spaces are subspace of '''R'''<sup>''n''</sup> and '''R'''<sup>''m''</sup> [[real coordinate space|real spaces]] respectively. But row and column spaces can be constructed from matrices with components in any [[field (mathematics)|field]] and even a [[ring (mathematics)|ring]].
 
==Overview==
Let A be a ''m''-by-''n'' matrix. Then
# rank(A) = dim(rowsp(A)) = dim(colsp(A)),
# rank(A) = number of pivots in any echelon form of A,
# rank(A) = the maximum number of linearly independent rows or columns of A.
 
If one considers the matrix as a [[linear transformation]] from '''R'''<sup>''n''</sup> to '''R'''<sup>''m''</sup>, then the column space of the matrix equals the [[image (mathematics)|image]] of this linear transformation.
 
The column space of a matrix A is the set of all linear combinations of the columns in A. If A = ['''a'''<sub>1</sub>, ...., '''a'''<sub>n</sub>], then colsp(A) = span {'''a'''<sub>1</sub>, ...., '''a'''<sub>n</sub>}.
 
The concept of '''row space''' generalises to matrices to '''C''', the field of [[complex number]]s, or to any [[field (mathematics)|field]].
 
Intuitively, given a matrix '''A''', the action of the matrix '''A''' on a vector '''x''' will return a linear combination of the columns of '''A''' weighted by the coordinates of '''x''' as coefficients. Another way to look at this is that it will (1) first project '''x''' into the '''row space''' of A, (2) perform an invertible transformation, and (3) place the resulting vector '''y''' in the '''column space''' of '''A'''. Thus the result ''' y =A x''' must reside in the '''column space''' of A. See the [[singular value decomposition]] for more details on this second interpretation.
 
==Example==
Given a matrix J:
:<math>
  J =
  \begin{bmatrix}
    2 & 4 & 1 & 3 & 2\\
    -1 & -2 & 1 & 0 & 5\\
    1 & 6 & 2 & 2 & 2\\
    3 & 6 & 2 & 5 & 1
  \end{bmatrix}
</math>
the rows are
'''r'''<sub>1</sub> = (2,4,1,3,2),
'''r'''<sub>2</sub> = (−1,−2,1,0,5),
'''r'''<sub>3</sub> = (1,6,2,2,2),
'''r'''<sub>4</sub> = (3,6,2,5,1).
Consequently the row space of J is the subspace of '''R'''<sup>5</sup> [[linear span|spanned]] by { '''r'''<sub>1</sub>, '''r'''<sub>2</sub>, '''r'''<sub>3</sub>, '''r'''<sub>4</sub> }.  
Since these four row vectors are [[Linear independence|linearly independent]], the row space is 4-dimensional.  Moreover in this case it can be seen that they are all [[orthogonality|orthogonal]] to the vector '''n''' = (6,−1,4,−4,0), so it can be deduced that the row space consists of all vectors in '''R'''<sup>5</sup> that are orthogonal to '''n'''.
 
==See also==
*[[Row space]]
*[[Column space]]
*[[null space]]
 
==External links==
{{wikibooks|Linear Algebra/Column and Row Spaces}}
*[http://mfile.akamai.com/7870/rm/mitstorage.download.akamai.com/7870/18/18.06/videolectures/strang-1806-lec06-20sep1999-80k.rm Lecture on column space and nullspace by Gilbert Strang of MIT]
*[http://wps.prenhall.com/am_leon_linearalg_7/53/13727/3514210.cw/content/index.html Row Space and Column Space]
 
==Notes==
{{reflist}}
 
[[Category:Abstract algebra]]
[[Category:Linear algebra]]

Latest revision as of 12:50, 30 July 2014

BMI Basics: The Body Mass Index is practical as a ballpark measuring. Health experts and organizations like the WHO, employ it to gain a standard idea of whether a individual is overweight, underweight, or is at a healthy weight, provided their height. If you're my age (which I'm not going to disclose,) we were possibly introduced to the BMI inside Middle School during PE. Back then I was taught to measure my BMI with a simple formula. A few punches found on the calculator plus voila, my body fat was quantified.

Free resource which you do not have to cognise how to puzzle out the bmi chart. The online tool does it for you. In order to do that you can choose some of the charts on this page. It won't take much time.

This way uses body fat scales which send a secure small bmi chart men electrical current by the body to calculate the amount of body fat tissue. Your body fat percentage is then calculated based on height, weight, age plus sex. It is a harmless method plus very exact. These scales are obtainable in the market and affordable.

Anorexia nervosa is an psychological disorder where the leading focus may be on food / the avoidance of food however it additionally deals with harmful methods of gaining perfection and a desire to control aspects. In a society that associates unreasonable thinness with beauty, there has been a marked escalation inside the amount of young adolescent women with anorexia. Many of them die due to starvation-related causes, suffer from bodily problems, or end up committing suicide. It is important to treat such people with psychotherapy, family therapy, and medication.

Besides the obvious weight and BMI measurements, you might wish to consider finding a model that has separate methods for male plus woman consumers. Weight distribution for people are different and scales which have a gender option might offer more exact readings.

I would like to share several insights plus tricks which bmi chart women I have learned along the method. Many of these women's running tips may apply to all runners, nevertheless they certainly take on a new perspective because the years go on plus you get elder, wiser, plus perhaps, quicker...

Obesity is not a single problem. There are several effects of weight. One of the initially plus foremost effects is inability to carry out day-to-day escapades. An fat individual is usually inactive and feels fatigued most of the time. Obesity gives birth to additional wellness issues. Some overweight persons develop Pickwick syndrome inside that a person feels drowsy plus color of his face remains reddish. Pain inside joints, bones, plus lower back part of the body is usually experienced by over-weight persons. Another chronic wellness issue which 1 can is susceptible to is diabetes that is incurable.

There is another method of calculating BMI for female in the event you do not want to convert feet and pounds to meters and kilograms. Take the earlier illustration of the woman weighing in at 150 pounds. Take the pounds that are 150 and instances it by 4.88 giving we 732, then derive the woman's height inside feet squared that is (5.5 occasions 5.5) that is 30.25 feet squared. Then hold on to these 2 results you merely got. Right after that, divide the weight by the height squared, in this case it would be (732 divided by 30.25) and the result is 24.1 that is really close to the earlier metric formula's outcome. See how simple it is very with regards to BMI calculations for women!