Invert vs. Transpose — What's the Difference?

To turn inside out or upside down

In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing another matrix, often denoted by AT (among other notations).The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley.

To reverse the position, order, or condition of

To reverse or transfer the order or place of; interchange.

To subject to inversion.

(Mathematics) To move (a term) from one side of an algebraic equation to the other side, reversing its sign to maintain equality.

To be subjected to inversion.

(Music) To write or perform (a composition) in a key other than the original or given key.

Something inverted.

To render into another language.

(Psychology) In early psychology, a person who displays behavior or attitudes considered typical of the opposite sex, including sexual attraction to members of one's own sex. No longer in scientific use.

To alter in form or nature; transform

(transitive) To turn (something) upside down or inside out; to place in a contrary order or direction.

(Music) To write or perform music in a different key.

To move (the root note of a chord) up or down an octave, resulting in a change in pitch.

To admit of being transposed.

To undergo inversion, as sugar.

A matrix formed by interchanging the rows and columns of a given matrix.

To divert; to convert to a wrong use.

(transitive) To reverse or change the order of (two or more things); to swap or interchange.

(anatomy) To turn (the foot) inwards.

To rewrite or perform (a piece) in another key.

A homosexual.

To move (a term) from one side of an algebraic equation to the other, reversing the sign of the term.

(architecture) An inverted arch (as in a sewer).

To rearrange elements in a matrix, by interchanging their respective row and column positional indicators.

The base of a tunnel on which the road or railway may be laid and used when construction is through unstable ground. It may be flat or form a continuous curve with the tunnel arch.

To give force to a directive by passing appropriate implementation measures.

(civil engineering) The lowest point inside a pipe at a certain point.

To reach a position that may also be obtained from a different move order.

(civil engineering) An elevation of a pipe at a certain point along the pipe.

A matrix with the characteristic of having been transposed from a given matrix.

A skateboarding trick where the skater grabs the board and plants a hand on the coping so as to balance upside-down on the lip of a ramp.

The resulting matrix, derived from performing a transpose operation on a given matrix.

(chemistry) Subjected to the process of inversion; inverted; converted.

(linear algebra) The process of rearranging elements in a matrix, by interchanging their respective row and column positional indicators.

To turn over; to put upside down; to upset; to place in a contrary order or direction; to reverse; as, to invert a cup, the order of words, rules of justice, etc.

To change the place or order of; to substitute one for the other of; to exchange, in respect of position; as, to transpose letters, words, or propositions.

To change the position of; - said of tones which form a chord, or parts which compose harmony.

To change; to transform; to invert.

To divert; to convert to a wrong use.

To bring, as any term of an equation, from one side over to the other, without destroying the equation; thus, if a + b = c, and we make a = c - b, then b is said to be transposed.

To undergo inversion, as sugar.

To change the natural order of, as words.

Subjected to the process of inversion; inverted; converted; as, invert sugar.

To change the key of.

An inverted arch.

A matrix formed by interchanging the rows and columns of a given matrix

Make an inversion (in a musical composition);

Change the order or arrangement of;

Turn inside out or upside down

Transfer from one place or period to another;

Cause to change places;

Transfer a quantity from one side of an equation to the other side reversing its sign, in order to maintain equality

Put (a piece of music) into another key

Transpose and remain equal in value;

Change key;