Website owner: James Miller
An interpretation of the product of two matrices
Suppose that the matrix A carries the vector X1 into the vector Y1, the vector X2 into the vector Y2 , etc. i.e.
AX1 = Y1
AX2 = Y2
......
......
AXn = Yn
Then
A [ X1 X2 .... Xn] = [Y1 Y2 ... Yn]
where [ X1 X2 .... Xn] is a matrix whose columns are X1, X2, .... , Xn and [Y1 Y2 ... Yn] is a matrix whose columns are Y1,Y2, ... ,Yn .
The above stated fact provides us with a way of viewing the product of one matrix by another. In the product
AB = C
the columns of B can be viewed as a set of vectors which are carried by the matrix A into the columns of C (i.e. the matrix A is viewed as an operator that operates on the columns of B, viewed as vectors, and carries them into the columns of C, also viewed as vectors).
In the same way B can be viewed as the operator matrix and the rows of A viewed as vectors which are carried into the rows of C (viewed as vectors).
Jesus Christ and His Teachings
Way of enlightenment, wisdom, and understanding
America, a corrupt, depraved, shameless country
On integrity and the lack of it
The test of a person's Christianity is what he is
Ninety five percent of the problems that most people have come from personal foolishness
Liberalism, socialism and the modern welfare state
The desire to harm, a motivation for conduct
On Self-sufficient Country Living, Homesteading
Topically Arranged Proverbs, Precepts, Quotations. Common Sayings. Poor Richard's Almanac.
Theory on the Formation of Character
People are like radio tuners --- they pick out and listen to one wavelength and ignore the rest
Cause of Character Traits --- According to Aristotle
We are what we eat --- living under the discipline of a diet
Avoiding problems and trouble in life
Role of habit in formation of character
Personal attributes of the true Christian
What determines a person's character?
Love of God and love of virtue are closely united
Intellectual disparities among people and the power in good habits
Tools of Satan. Tactics and Tricks used by the Devil.
The Natural Way -- The Unnatural Way
Wisdom, Reason and Virtue are closely related
Knowledge is one thing, wisdom is another
My views on Christianity in America
The most important thing in life is understanding
We are all examples --- for good or for bad
Television --- spiritual poison
The Prime Mover that decides "What We Are"
Where do our outlooks, attitudes and values come from?
Sin is serious business. The punishment for it is real. Hell is real.
Self-imposed discipline and regimentation
Achieving happiness in life --- a matter of the right strategies
Self-control, self-restraint, self-discipline basic to so much in life