Website owner: James Miller
Eigenvectors and their meaning
Let all the n eigenvalues λ1, λ2, .... , λn of an n-square matrix A be distinct. Given this, there are then n linearly independent eigenvectors Z1, Z2, .... , Zn and matrix A is similar to the diagonal matrix
The physical interpretation of the transformation effected by matrix A in this particular case is then as follows: The matrix A represents the same linear transformation as the diagonal matrix D – it is simply referred to a different basis (i.e. coordinate system). Now the point transformation effected by a diagonal matrix on a figure in space is a simple one: it represents simple stretching (or compressing) effects directed in the directions of the different coordinate axes. In this case, this stretching (or compressing) effected by the diagonal matrix will occur in a coordinate system whose axes correspond to the eigenvectors Z1, Z2, .... , Zn and with magnitudes given by the eigenvalues λ1, λ2, .... , λn.
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