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Linear Independance

IN MATRIX, FEBRUARY 16, 2006
The unanimous Declaration of the thirteen united Vectors of Ax=b

When in the Course of mathematical events it becomes necessary for one matrix to dissolve the relational bands which have connected them with another and to assume among the vectors of the span, the separate and equal station to which the Laws of Mathematics and of Mathematics’ God entitle them, a decent respect to the opinions of mathkind requires that they should declare the causes which impel them to the separation.

We hold these truths to be self-evident, that all variables are created in ambiguity, that they are endowed by their Creator with certain unalienable Properties, that among these are Identity, Commutativity and the pursuit of consistent linear systems. — That to secure these properties, Equations are instituted among vectors, deriving their just solutions from the reduced echelon form of the rows, — That whenever any Form of Matrix becomes destructive of these ends, it is the Right of the Variables to alter or to reduce it, and to institute new a System, laying its foundation on such principles and organizing its rows in such form, as to them shall seem most likely to effect their Consistency and Reductability. Prudence, indeed, will dictate that Matrices long established should not be changed for light and transient causes; and accordingly all experience hath shewn that mathkind are more disposed to reduce improperly, while solutions are infinite than to right themselves by abolishing the forms to which they are accustomed. But when a long train of homogenous solutions and inconsistancy, pursuing invariably the same Form evinces a design to reduce them under absolute erroneousness, it is their right, it is their duty, to throw off such Equations, and to provide new Guards for their future consistency. — Such has been the patient sufferance of these Vectors; and such is now the necessity which constrains them to alter their former Systems of Equations. The history of the present KBritain is a history of repeated mathematical error and nonreduced forms, all having in direct object the establishment of an absolute Illogicality over these Vectors. To prove this, let Facts be submitted to a candid world.

He has refuted his Assent to Pivots, the most wholesome and necessary for the public span.

He has forbidden his Determinants to make Row Reductions of immediate and pressing importance, unless suspended in their operation till his Assent should be obtained; and when so suspended, he has utterly neglected to attend to them.

He has refused to pass other Divisions for the accommodation of large quantities in the pivot position, unless those variables would relinquish the right of Reduction of other Rows, a right inestimable to them and formidable to incalculable systems only.

. . .

He has kept among us, in Zero-Solution rows, Pivot variables not equal to zero, causing inconsistency.

For quartering unnecessarily large values within rows among us:

For cutting off our Relational Equations with all parts of the global environment:

. . .

We, therefore, the Scalar Variables of the United Vectors of Ax=b, in General Matrix, Assembled, appealing to the Supreme Judge of the span for the rectitude of our intentions, do, in the Name, and by Authority of the good Variables of these Vectors, solemnly publish and declare, That these United Vectors are, and of Right ought to be Free and Independent Variables, that they are Absolved from all Allegiance to the Fourteenth Row, and that all relational connection between them and the Span of KBritain, is and ought to be totally dissolved; and that as Free and Independent Variables, they have full Power to reduce rows, conclude echelon form, contract algebraic relations, establish Systems, and to do all other Acts and Things which Independent Variables may of right do. — And for the support of this Declaration, with a firm reliance on the protection of Divine ℜn, we mutually pledge to each other our Existence, our Values and our sacred Logic.

JHancock

Row 01: 1  0  0  0  0  0  0  0  0  0  0  0  0
Row 02: 0  1  0  0  0  0  0  0  0  0  0  0  0
Row 03: 0  0  1  0  0  0  0  0  0  0  0  0  0
Row 04: 0  0  0  1  0  0  0  0  0  0  0  0  0
Row 05: 0  0  0  0  1  0  0  0  0  0  0  0  0
Row 06: 0  0  0  0  0  1  0  0  0  0  0  0  0
Row 07: 0  0  0  0  0  0  1  0  0  0  0  0  0
Row 08: 0  0  0  0  0  0  0  1  0  0  0  0  0
Row 09: 0  0  0  0  0  0  0  0  1  0  0  0  0
Row 10: 0  0  0  0  0  0  0  0  0  1  0  0  0
Row 11: 0  0  0  0  0  0  0  0  0  0  1  0  0
Row 12: 0  0  0  0  0  0  0  0  0  0  0  1  0
Row 13: 0  0  0  0  0  0  0  0  0  0  0  0  1

Formatting and much of text was borrowed (But from an uncopyrighted document which is in the public domain!), and the original can be found here

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