Website owner: James Miller
In linear transformations between abstract n-dimensional vector spaces the operators are always matrices
In linear transformations between or within abstract finite dimensional vector spaces the operators are always matrices. Why? Because of the role that matrices play in representing linear transformations in these spaces. Matrices containing the coordinate vectors of basis vectors are the means utilized to define linear transformations between two abstract finite dimensional spaces.
Because of this, when we talk about the sum of two linear transformations or the product of a linear transformation by a scalar, we are really talking about the sum of two matrices or the product of a scalar times a matrix.
Note that there is a conceptual difference between an operator and a linear mapping or linear transformation. An operator, such as a matrix, is conceived as an object. You can do operations on objects like matrices. A linear mapping or linear transformation is a functional assignment. It doesn't make sense to do operations such as addition on functional assignments.
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